Identifier
Mp00124:
Dyck paths
—Adin-Bagno-Roichman transformation⟶
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]=>[1,0,1,0]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,1,0,0]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[2,3,1]=>[[.,[.,.]],.]
[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]=>[1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[.,[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[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]=>[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[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]=>[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[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]=>[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[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]=>[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[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]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[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]=>[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
[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]=>[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[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]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[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]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[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]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[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]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[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]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[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]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[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]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[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]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[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]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[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]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[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]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[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]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[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]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[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]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[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]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,1,8,2]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,1,3]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,1,2,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,1,7,8,2]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,3]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,1,3,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,1,2,8,3]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,7,1,8,2,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,1,2,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,2]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,1,7,8,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,1,7,2,8,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,6,1,7,8,3]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,7,1,8,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,1,5]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,1,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,7,1,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,1,3,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,1,2,7,8,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,1,2,8,3,4]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,5,6,1,7,2,8,4]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,1,7,8,2,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,7,1,2,8,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,6,7,1,8,2,5]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,6,7,8,1,2,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,1,2,3,8,4]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,6,7,1,2,8,3,5]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,1,6,7,2,8,3]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,6,1,7,8,2,3,4]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,1,6,2,7,8,3]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,5,1,6,7,2,8,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,6,1,7,2,3,8,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,6,1,7,8,2,3,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,5,6,1,7,8,3,4]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,6,7,1,8,3,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,6,7,1,8,4,5]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,1,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,1,5,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,7,8,1,4,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,5,6,1,3,7,8,4]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,5,1,7,8,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,1,3,8,5]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,7,8,1,3,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,5,7,1,8,3,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,6,7,8,3]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,1,2,7,8,3,4]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1,2,7,3,8,4]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,6,1,2,7,8,3,5]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,7,1,2,8,3,4,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,5,1,6,2,7,8,4]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,6,7,2,8,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,6,1,7,2,4,8,5]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,7,1,8,2,4,5,6]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,5,6,1,2,7,8,4]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,6,1,7,2,8,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,5,1,7,8,2,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,6,7,1,2,8,5]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,7,8,1,2,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,6,7,1,2,4,8,5]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,7,8,4]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,1,2,3,8,4,5]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,7,8,3,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,7,1,2,8,3,5,6]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,6,7,1,2,3,8,5]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,8,5]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[5,7,1,2,3,8,4,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,7,1,8,2,3,4,6]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,2]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,2,3]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,8,2,4]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,2,3,4]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,2,8,3,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,4,6,7,8,2,5]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,6,7,8,2,3,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,7,2,8,3,4,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,6,2,7,8,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,1,6,7,2,8,4,5]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,7,2,8,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4,5,7,8,2,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,7,8,2,4,6]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,1,7,2,3,8,4,5]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,1,7,2,8,3,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,6,7,2,3,8,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,5,7,2,8,3,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,7,8,2,3,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,7,2,3,4,8,5]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,7,2,3,8,4,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,7,2,8,3,4,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,7,8,2,3,4,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,3]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,1,6,7,3,8,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,6,1,7,8,3,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,5,1,6,3,7,8,4]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,7,8,3,5,6]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,6,1,7,3,4,8,5]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,7,8,3,4,6]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,1,7,8,4,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,6,1,7,8,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,4,7,1,8,5,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,7,1,8,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,8,1,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,8,1,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,4,7,1,5,8,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,8,5,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,8,1,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,7,4,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,5,1,6,8,4,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,6,1,8,4,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,8,1,4,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,1,4,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,1,3,7,8,4,5]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,6,1,3,7,4,8,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,7,8,4,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,7,1,3,8,4,5,6]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,7,3,8,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,5,8,3,6,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,7,3,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,8,3,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,5,1,7,3,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,5,1,6,8,3,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,6,1,8,3,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,6,8,1,3,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,8,1,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,1,3,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,5,1,3,8,4,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,5,1,6,8,3,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,5,1,8,3,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,5,7,1,3,4,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,5,6,1,3,8,4,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,8,4,5,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,3]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,6,7,8,3,4]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,1,2,7,8,3,4,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,6,3,7,8,4]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,1,2,7,3,8,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,7,3,8,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,5,7,8,3,6]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,1,2,7,8,3,5,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,7,3,8,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,7,8,3,4,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,7,8,4,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,7,2,8,4,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,6,2,7,8,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,7,2,8,6]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,6,8,2,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4,5,8,2,6,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,7,2,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,8,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,8,2,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,6,8,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,5,6,8,2,4,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,7,2,4,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,8,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,6,1,2,7,8,4,5]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,6,1,2,7,4,8,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,7,8,4,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,7,1,2,8,4,5,6]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,6,2,7,8,5]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,4,1,5,7,2,8,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,5,6,8,2,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,5,8,2,6,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,8,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,6,1,2,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,5,7,1,2,8,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,6,1,8,2,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,6,8,1,2,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,4,7,1,2,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,7,1,2,4,8,5,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,5,1,2,8,4,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,1,6,8,2,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,7,1,2,4,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,5,6,1,2,8,4,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,8,4,5,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,7,8,4,5]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,7,8,4,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[7,1,2,3,8,4,5,6]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,6,3,7,8,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,5,6,8,3,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,5,8,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,7,2,3,8,5,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,5,2,6,8,3,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,8,3,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,5,6,2,8,3,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,7,2,3,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,8,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[4,7,1,2,3,8,5,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,7,3,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,6,8,3,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,5,1,2,8,3,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,5,1,7,2,3,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,5,1,6,8,2,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,5,1,8,2,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,6,1,2,8,3,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,7,1,2,3,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,8,3,5,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,7,8,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,8,5,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,6,8,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,8,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,6,3,8,4,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,1,2,6,8,3,4,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,7,2,3,4,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[5,1,6,2,3,8,4,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,1,6,2,8,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[5,1,8,2,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,8,4,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,6,1,2,8,3,4,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,6,1,8,2,3,4,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,8,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,8,4,5,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,2,3]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,2,8,3]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,2,7,8,3]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,6,7,2,8,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,7,2,8,4]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,2,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,5,6,7,2,3,8,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,6,7,2,8,3,5]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,6,7,8,2,3,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,5,2,6,7,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,6,2,7,8,3,4]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,6,2,7,8,3,5]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,6,7,2,8,5]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,7,8,2,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,4,7,8,2,5,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,6,7,2,4,8,5]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,7,2,8,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,7,8,2,4,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,6,2,3,7,8,4]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,7,2,3,8,4,5]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,7,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,7,8,2,3,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,7,8,2,3,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,6,7,2,3,4,8,5]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,2,3,8,4,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,3]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,6,2,7,8,3,4,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,2,6,3,7,8,4]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,2,7,8,3,5,6]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,6,2,7,3,4,8,5]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,7,8,3,4,6]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,6,2,7,8,4,5]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,2,7,4,8,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,7,8,4,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,8,2,7]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,5,8,2,6,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,4,7,2,5,8,6]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,8,2,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,7,2,4,8,5,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,7,4,8,6]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,6,8,4,7]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,7,2,4,8,6]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,5,6,2,8,4,7]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,8,2,4,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,7,2,4,5,8,6]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,8,5,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,6,7,8,4]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,3,7,8,4,5]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,6,2,3,7,4,8,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,7,2,3,8,4,5,6]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,5,7,3,8,6]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,5,8,3,6,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,2,7,3,5,8,6]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,8,3,5,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,6,2,3,7,8,5]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,7,2,3,8,5,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,5,2,7,3,8,6]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,5,2,6,8,3,7]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,4,5,7,2,3,8,6]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,6,8,2,3,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,7,2,3,5,8,6]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,8,5,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,7,8,5]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,7,4,8,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,5,2,3,8,4,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,7,3,4,8,6]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,2,6,8,3,4,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,5,7,2,3,4,8,6]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,6,2,3,8,4,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,8,6]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,8,4,5,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,6,7,8,3,5]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,6,3,7,8,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,4,7,8,3,5,6]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,6,3,7,8,4,5]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,7,8,4,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,1,7,3,8,4,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,6,3,7,8,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,6,8,3,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,7,3,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,8,3,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,1,7,3,4,8,5,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,5,3,6,8,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,1,5,3,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,1,5,6,8,3,4,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,1,5,8,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,7,3,4,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,1,6,3,8,4,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,1,6,8,3,4,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,7,8,4,5,6]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,7,4,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,8,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,1,7,8,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,1,7,5,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,1,8,6,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,4,1,5,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,4,6,1,7,5,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,7,1,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,4,1,7,5,6,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,1,4,8,5,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,5,1,4,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,6,4,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,5,6,1,7,4,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,7,1,4,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,4,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,1,6,4,5,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,6,1,4,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,1,4,7,5,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,6,7,8,4,5]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,1,3,7,8,4,5,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,1,3,7,4,8,5,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,5,8,4,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,1,3,6,4,8,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,8,5,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,3,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,3,5,8,6,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,6,3,7,5,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,6,3,5,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,3,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,8,5,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,5,3,7,8,6]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,4,1,5,6,3,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,5,6,7,3,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,5,6,3,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,3,6,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,3,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,5,1,6,3,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,6,1,3,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,6,1,7,3,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,1,3,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,1,3,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,3,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,6,3,5,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,6,1,3,7,5,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,6,1,3,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,1,3,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,1,3,4,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,1,5,3,6,7,4,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,1,5,6,3,7,4,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,5,6,7,3,4,8]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,5,3,4,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,5,3,4,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,5,1,3,6,4,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,1,3,6,4,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,5,1,6,3,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,6,3,7,4,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,5,1,6,7,3,4,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,5,6,1,3,7,4,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,1,3,6,4,5,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,7,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,6,1,7,3,4,5,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,1,3,4,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,3,4]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,2,5,6,7,3,8,4]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,2,5,6,3,7,8,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,2,6,7,3,8,4,5]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,7,8,3,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,4,7,8,3,5,6]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,2,6,7,3,4,8,5]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,2,5,7,3,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,2,5,7,8,3,4,6]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,4]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,2,6,3,7,8,4,5]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,2,6,3,7,4,8,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,7,8,4,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,4,7,3,8,5,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,7,3,8,6]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,6,8,3,7]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,4,5,8,3,6,7]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,7,3,5,8,6]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,8,5,7]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,8,3,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,2,6,3,4,7,8,5]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,2,7,3,4,8,5,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,7,4,8,6]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,2,5,7,3,4,8,6]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,5,6,3,8,4,7]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,2,5,6,8,3,4,7]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,8,5,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,7,8,4,5]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,2,6,7,4,8,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,5,8,4,6,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,6,8,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,4,2,7,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,2,7,5,8,6]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,2,8,6,7]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,2,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,4,2,5,8,6,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,6,2,7,5,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,7,2,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,4,7,5,8,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,2,4,8,5,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,5,2,4,8,6,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,5,2,6,4,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,5,2,6,7,4,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,5,6,2,4,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,7,2,4,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,5,2,4,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,2,4,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,2,6,7,4,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,7,4,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,6,2,4,5,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,6,7,8,4,5]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,2,7,8,4,5,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,2,6,4,7,8,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,2,7,4,8,5,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,5,6,8,4,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,5,8,4,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,1,2,6,8,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,4,2,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,4,2,8,5,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,5,2,7,8,6]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,2,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,2,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,2,5,8,6,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,6,7,5,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,4,2,7,5,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,4,1,2,7,5,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,8,5,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1,2,8,5,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,5,6,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,5,6,7,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,5,6,2,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,5,2,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,5,1,2,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,5,1,6,2,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,2,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,1,2,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,1,7,2,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,1,2,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,5,1,2,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,4,1,2,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,6,2,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,6,7,2,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,6,1,2,7,5,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,7,1,2,5,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1,2,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,1,2,7,5,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,2,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,2,4,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,5,6,7,4,8]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,5,2,4,8,6,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,5,6,2,4,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,5,1,2,4,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,6,4,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,6,2,7,4,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,5,1,6,7,2,4,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,5,1,6,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,5,6,1,2,7,4,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,5,6,1,2,4,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,5,1,2,4,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,2,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,7,5,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,1,2,6,4,7,5,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,6,2,4,7,5,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,6,1,2,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,2,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,1,2,4,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,2,7,4,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,4,5]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,3,6,7,4,8,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,7,8,4,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,7,8,4,5,6]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,6,4,7,8,5]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,7,4,8,6]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,8,4,7]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,5,8,4,6,7]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,7,4,5,8,6]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,6,8,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,4,3,7,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,3,7,5,8,6]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,4,5,3,8,6,7]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,6,3,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,7,3,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,3,5,8,6,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,6,3,7,5,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,2,3,7,5,8,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,2,3,8,5,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,5,6,7,3,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,5,3,6,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,5,2,3,8,6,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,5,2,6,3,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,5,2,6,7,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,6,2,7,3,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,2,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,2,3,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,6,7,5,8]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,6,7,3,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,6,2,3,5,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,4,2,3,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,3,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,8,5,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,5,3,7,8,6]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,5,3,8,6,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,5,6,7,3,8]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3,7,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,5,2,3,8,6,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,5,2,6,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,5,6,2,3,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,5,2,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,5,1,2,3,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,6,3,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,5,1,6,2,3,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,6,2,7,3,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,1,6,2,3,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,1,2,7,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,6,1,7,2,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,2,3,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,6,7,5,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,6,7,3,5,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,6,2,3,7,5,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,6,2,7,3,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,6,7,2,3,5,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,6,2,3,5,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,6,7,1,2,3,5,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,6,1,2,3,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,1,2,3,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,3,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,1,2,7,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,6,8,5,7]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4,8,6,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,5,3,6,4,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,2,5,6,3,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,2,5,6,3,7,4,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,2,5,3,4,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,5,3,4,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,6,4,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,6,7,4,8]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,6,4,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,5,2,6,3,4,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,2,6,7,3,4,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,5,6,2,3,4,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,5,2,3,4,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,1,2,3,4,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2,3,6,7,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,6,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,1,2,6,3,7,4,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,6,7,3,4,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,6,3,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,1,6,2,3,7,4,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,1,6,2,7,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[5,1,6,2,3,4,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,1,7,2,3,4,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,6,7,4,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,2,6,3,4,7,5,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,2,6,3,7,4,5,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,3,4,5,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,2,3,7,4,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,7,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[6,1,2,3,7,4,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[6,1,2,7,3,4,5,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,7,5,6,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,9,1,2,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[6,9,1,2,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,10,1,2,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,5,9,8]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,7,9,1,2,3,4,5,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,9,1,2,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,7,1,9,2,3,4,5,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,10,1,2,3,4,5,6,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,9,1,2,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,4,7,5,6,9,8]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,9,1,2,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[5,10,1,2,3,4,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,9,7,8]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,9,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,7,9,1,2,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[4,10,1,2,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,9,7,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,10,1,2,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,10,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,8,9,1,2,3,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,9,10,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,6,1,2,3,4,9,7,8]=>[[.,[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,8,1,9,2,3,4,5,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[5,8,9,1,2,3,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,1,7,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,7,6,8,9]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,6,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,6,5,7,8,9]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,5,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,4,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,8,3,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,5,8,6,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,8,1,3,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,1,3,5,7,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,4,1,7,3,8,5,6,9]=>[[.,[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,1,3,4,5,8,6,7,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,2,9]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,7,2,8,9]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,2,4,6,7,8,9]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,8,2,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,2,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,8,2,9]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,1,6,2,7,8,9]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,6,1,7,2,8,9]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,1,2,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,5,3,6,7,8,9]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,3,5,6,8,9]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,3,6,7,8,9]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,7,1,2,8,3,9]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,6,7,8,1,2,3,5,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[4,1,2,3,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,8,4,9]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,4,7,8,9]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,6,2,7,3,8,4,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,7,1,8,2,3,4,9]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,5,8,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,8,1,2,3,4,5,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,8,6,9]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,4,7,5,8,6,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,4,7,8,5,6,9]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,1,2,3,4,5,8,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,1,2]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,1,3]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,1,4]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,1,5]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,1,6]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,1,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,9,1,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,6,7,9,2,8]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,10,11,1,3]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,9,1,2,4]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,5,6,7,9,2,8]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,11,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,9,2,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,9,10,1,2,4]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,9,1,2,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,5,6,1,8,9,2,7]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,9,1,2,3,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,7,8,9,1,2,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,9,10,1,2,4,5]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,9,1,2,5,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,6,8,9,1,2,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,9,10,1,2,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,8,9,1,2,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,8,9,10,1,2,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,4,5,8,9,10,1,2,6,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,9,1,2,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,1,2,3,4,7,9,5,8]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,7,9,1,2,3,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,9,10,1,2,7,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,10,1,2,3,4,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,7,10,1,2,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,7,8,10,1,2,3,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,1,9,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,2]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,8,1,9,2,3]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,8,1,2,9,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,2]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,7,1,8,2,9,3]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,8,1,9,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,7,1,2,8,9,3]=>[[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,2]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,8,1,9,2,3,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,5,6,1,2,7,8,9,3]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,8,1,2,3,4,9,5]=>[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,6,1,7,8,9,2,3,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[7,8,1,9,2,3,4,5,6]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,5,1,2,6,7,8,9,3]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,6,1,2,3,7,8,9,4]=>[[.,[.,.]],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,8,1,2,3,4,5,9,6]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,9,2,3]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,9,2,3,4]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[7,1,8,9,2,3,4,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,7,2,8,3,9,4,5]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,9,2,3,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,9,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,9,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,2,3,7,4,8,9,5]=>[[.,.],[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[8,1,2,3,9,4,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,7,8,9,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,9,5,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,9,6,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,2,3]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,8,2,9,3]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,9,2,3,4]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,9,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,6,7,8,2,9,3,4,5]=>[.,[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,7,8,9,2,3,4,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,9,3]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,9,3,4]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,2,7,3,8,4,9,5]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,8,2,9,3,4,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,9,6,7]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,9,7]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,9,4]=>[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[1,2,8,3,4,5,6,9,7]=>[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,3,6,4,7,8,9,5]=>[.,[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,2,3,8,4,5,9,6,7]=>[.,[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,5]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,4,7,5,8,9,6]=>[.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,4,8,5,6,9,7]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,8,6,9,7]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,1,10,2]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,8,1,9,10,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,8,9,1,10,2,3]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,8,9,1,2,10,3]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,10,2]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,7,8,1,9,2,10,3]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,10,2]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,10,2]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,5,6,1,7,8,9,10,2,3]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,10,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,6,1,2,3,7,8,9,10,4]=>[[.,[.,.]],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,9,1,2,3,4,5,6,10,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,9,10,2,3,4]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,1,8,2,9,3,10,4,5,6]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,9,10,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[7,1,2,8,3,9,4,10,5,6]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,7,8,9,10,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,8,9,10,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,9,10,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,10,7,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,10,2,3]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,9,10,2,3,4]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,9,10,2,3,4,5]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,7,8,9,10,2,3,4,5,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,7,2,8,3,9,4,10,5,6]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,10,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[1,2,9,3,4,5,6,7,10,8]=>[.,[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,10,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,10,5]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,10,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,4,5,9,6,7,10,8]=>[.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,10,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,6,9,7,10,8]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,4]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,5]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,10,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,9,4]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,10,4]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,10,5]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,10,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,10,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,9,10,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,10,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,8,9,2,4]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,9,3,4]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,7,1,2,9,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,6,1,2,8,9,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,1,2,7,8,9,6]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,9,5]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,9,4]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,5,6,1,2,9,7,8]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,1,2,9,4,5,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,1,2,3,9,5,6,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,9,6,7,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,9,4]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,9,3]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,1,7,8,9,5,6]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,5,2,6,7,8,9,4]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,7,8,10,1,2,3,4,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,9,1,7,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,6,1,9,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,9,2,8]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,1,9,6,7,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,9,6,8]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,4,7,9,5,6,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,9,10,4]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,7,8,1,9,3,4]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,5,1,8,6,9,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,7,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,9,6,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,7,3,8,4,9,5,10,6]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,9,10,1,2,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,7,8,1,2,3,4,10,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,8,9,1,3,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,9,1,3,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,9,1,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,9,1,3,4]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,9,2,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,7,8,1,2,9,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,9,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,8,10,2,9]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,6,7,9,3,8]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,7,8,1,2,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,10,1,11,2]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,1,9,3]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,9,1,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,9,1,10,3]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,1,8,9,6,7]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,8,9,1,6,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,8,1,9,10,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,8,9,1,10,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,11,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,8,1,9,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,1,9,4,5,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,8,9,10,1,2,3,4,5,11,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,9,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,5,1,6,7,9,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,6,8,9,2,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,9,1,3,5]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,8,9,2,3,4,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,6,7,8,9,2,3,5]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,10,1,4,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,5,6,1,7,8,9,10,3]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,9,10,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,9,4]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,10,6,7,8,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,9,1,10,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,6,1,7,8,9,10,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,6,1,7,8,9,10,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,9,10,1,3,4]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,9,5]=>[[.,.],[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,9,1,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,9,5,7,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,7,8,9,2,3,4,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,2,4,7,6,9,8]=>[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,6,8,9,7]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,7,8,9,2,4,5,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,7,8,9,10,11,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,8,1,3,4,5,6,9,7]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,4,5,8,1,6,9,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,9,4,5]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,7,8,1,9,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,5,6,1,7,2,9,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,1,8,9,3,4,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,7,9,8]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,6,7,1,9,2,3,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,9,5,8]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,9,7,10]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,8,9,6,10]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,8,3,9,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,9,6,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,9,6,8]=>[.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,9]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,5,1,2,3,9,6,7,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,7,1,8,9,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,5,7,9,1,2,4,6,8,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,9,1,4,5]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,10,7,9]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,10,7,9]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,8,2,9,3,10,4,11,5,12,6,7]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,12,9,11]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,6,8,2,9,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,6,7,9,2,10,8]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[[.,.],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,1,7,8,9,3,4,5,6]=>[[.,.],[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,10,7,9]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,9,1,6,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,2,7,4,6,9,8]=>[.,[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,1,3,4,5,9,6,7,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5,11]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,2,3,7,6,9,8]=>[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,4,6,8,1,3,5,7,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,10,11,12,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,8,6,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,9,10,1,7,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,8,9,10,1,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,9,10,1,5,6]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,9,10,1,4,5]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,6,10,1,7,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,1,6,2,7,3,9,4,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,9,6,8]=>[.,[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9,10]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,8,6,9,10]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,5,6,7,1,8,2,10,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,11,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,8,9,10,1,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,9,10,1,3,4,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,1,12,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[[.,.],.]]
Map
Adin-Bagno-Roichman transformation
Description
The Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.
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
Sorry, this map was not found in the database.