Identifier
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00027: Dyck paths —to partition⟶ Integer partitions
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-1Cc0002;cc-rep-2
[.,.]=>[1,0]=>[]
[.,[.,.]]=>[1,1,0,0]=>[]
[[.,.],.]=>[1,0,1,0]=>[1]
[.,[.,[.,.]]]=>[1,1,1,0,0,0]=>[]
[.,[[.,.],.]]=>[1,1,0,1,0,0]=>[1]
[[.,.],[.,.]]=>[1,0,1,1,0,0]=>[1,1]
[[.,[.,.]],.]=>[1,1,0,0,1,0]=>[2]
[[[.,.],.],.]=>[1,0,1,0,1,0]=>[2,1]
[.,[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0]=>[]
[.,[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0]=>[1]
[.,[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0]=>[1,1]
[.,[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0]=>[2]
[.,[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0]=>[2,1]
[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]=>[1,1,1]
[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]=>[2,1,1]
[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]=>[2,2]
[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]=>[2,2,1]
[[.,[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0]=>[3]
[[.,[[.,.],.]],.]=>[1,1,0,1,0,0,1,0]=>[3,1]
[[[.,.],[.,.]],.]=>[1,0,1,1,0,0,1,0]=>[3,1,1]
[[[.,[.,.]],.],.]=>[1,1,0,0,1,0,1,0]=>[3,2]
[[[[.,.],.],.],.]=>[1,0,1,0,1,0,1,0]=>[3,2,1]
[.,[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>[]
[.,[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,0,0]=>[1]
[.,[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]
[.,[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,0,0]=>[2]
[.,[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]
[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]
[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]
[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]
[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]
[.,[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,0]=>[3]
[.,[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]
[.,[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]
[.,[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]
[.,[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]
[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]
[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]
[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]
[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]
[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]
[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]
[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]
[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]
[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]
[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]
[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]
[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]
[[.,[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,0,1,0]=>[4]
[[.,[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]
[[.,[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]
[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]
[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]
[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]
[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]
[[[.,[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]
[[[[.,.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]
[[[[.,[.,.]],.],.],.]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]
[[[[[.,.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[]
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2]
[.,[.,[.,[[[.,.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]
[.,[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[3]
[.,[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]
[.,[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]
[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]
[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]
[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]
[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]
[.,[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]
[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[4]
[.,[[.,[.,[[.,.],.]]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]
[.,[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]
[.,[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]
[.,[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]
[.,[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]
[.,[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]
[.,[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]
[.,[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]
[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]
[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]
[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]
[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]
[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]
[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]
[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]
[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]
[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]
[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]
[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[4,3,2,2,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]
[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]
[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]
[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[4,3,3,2,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]
[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]
[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[4,4,2,1,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]
[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,4,2,2,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]
[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[4,4,3,1,1]
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[4,4,3,2]
[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[4,4,3,2,1]
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5]
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]
[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]
[[.,[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]
[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]
[[.,[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]
[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]
[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]
[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]
[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]
[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]
[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[5,3,2,2,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]
[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,3,1,1]
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[5,3,3,2]
[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,3,3,2,1]
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]
[[[.,[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]
[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]
[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,1]
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[5,4,2,2]
[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[5,4,2,2,1]
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]
[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,1]
[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,1]
[[[[[.,[.,.]],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2]
[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2]
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1,1]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2,1]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1,1]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2,1]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1,1]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2,1]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1,1]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1,1]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2,1]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1,1]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2,1]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2,1]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1,1]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2,1]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2,1]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1,1]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2,1]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2,1]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3]
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1,1]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,1]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[6]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1,1]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1,1]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1,1]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1,1]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1,1]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,1,1]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1,1]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1,1,1]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1,1]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1,1]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1,1]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1,1]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1,1]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1,1]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1,1]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1,1]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,1,1]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1,1]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1,1]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1,1]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1,1]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1,1]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1,1]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1,1]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1,1]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1,1]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,1,1]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1,1]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1,1]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1,1]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1,1]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1,1]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1,1]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1,1]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1,1]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1,1]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1,1]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1,1]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1,1]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1,1]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,2]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,2]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,2]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,2]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,2]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,2]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,2]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,2]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,2]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,2]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,2]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,2]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,2]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,2]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,2]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,2]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,2]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2,1]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2,1]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2,1]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,2,1]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,2,1]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,2,1]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,2,1]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2,1]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,2,1]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,2,1]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,2,1]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,2,1]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,2,1]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2,1]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,2,1]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,2,1]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2,1]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,2,1]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,2,1]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,2,1]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,2,1]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2,1]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,2,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2,1]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,1]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,1]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,1]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,1]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,1]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1,1]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,1,1]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,1,1]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,1,1]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,1,1]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,1,1]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,1,1]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,1,1]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,1,1]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,1,1]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,1,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,1,1]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,1,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,2]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,2]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,2]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,2]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,2]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,2]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,2]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,2,1]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,2,1]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,2,1]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,2,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,2,1]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,2,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,2,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1,1]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,1]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,1]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1,1]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1,1,1]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1,1,1]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1,1,1]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1,1,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,1,1]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,1,1]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,1,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,2]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,2]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,2]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2,1]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,2,1]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,2,1]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,2,1]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,2,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,1]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,1]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,1]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1,1]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,1,1]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,1,1]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,1,1]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,1,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,2]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,2]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,2]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2,1]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,2,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,2,1]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,2,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1,1]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1,1]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1,1]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,1]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1,1]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1,1]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,1]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1,1,1]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1,1,1]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1,1]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1,1,1]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,1,1]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,1,1]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1,1,1]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1,1,1]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1,1]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,1,1]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,2]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,2]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,2]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,2]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,2,1]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,2,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,2,1]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,2,1]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,1]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,1]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,1,1]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,1,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,2]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,2]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,2,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,2,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1,1]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1,1,1]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1,1]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1,1]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,1,1]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,2]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,2]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,2,1]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,2,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,1,1]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1,1]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,2]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,2,1]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1,1]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1,1]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,1]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1,1]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,1]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1,1]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,1]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1,1]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1,1,1]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1,1,1]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,1,1]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1,1,1]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,1,1]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1,1,1]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1,1,1]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1,1,1]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,2]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,2]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,2,1]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,2,1]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,2,1]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,2,1]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,1]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,1]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,1,1]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,1,1]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,2]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,2,1]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,2,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,1]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1,1,1]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,2,1]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,1]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,1,1]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,2]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,1]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1,1]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1,1,1]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1,1,1]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,1,1]
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1,1,1]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,2]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,2,1]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,2,1]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,1]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,1,1]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,2]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,2,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1,1]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,1]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,1,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,2]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,2,1]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1,1]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]
[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1]
[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,1]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1,1]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1,1]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,1]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1,1]
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1,1]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1,1]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,1]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,1]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,1]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1,1]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1,1]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,1]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,1]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1,1]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1,1]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1,1]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1,1]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1,1]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,1,1]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,1,1]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,1,1]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1,1,1]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1,1,1]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1,1]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1,1]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1,1,1]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1,1,1]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1,1,1]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1,1]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1,1]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1,1,1]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1,1,1]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,1,1]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,1,1]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1,1,1]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,1,1]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1,1,1]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1,1]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,1,1]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,1,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,1]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,2]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,2]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,2]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,2]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,2]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,2]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,2]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,2]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,2]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,2]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,2]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,2]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,2]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,2,1]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,2,1]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,2,1]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,2,1]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,2,1]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,2,1]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,2,1]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,2,1]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,2,1]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,2,1]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,2,1]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,2,1]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,2,1]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,1]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,1]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,1]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,1]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,1]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,1,1]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,1,1]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,1,1]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,1,1]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,1,1]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,2]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,2]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,2]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,2]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,2]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,2,1]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,2,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,2,1]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,2,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,2,1]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1,1]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,1]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,1]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1,1,1]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1,1,1]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,1,1]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,1,1]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,2]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,2]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,2,1]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,2,1]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,1]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,1,1]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,1,1]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,2]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,2]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,2,1]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,2,1]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1,1]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1,1]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,1]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1,1]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,1]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1,1,1]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1,1,1]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,1,1]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1,1,1]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,1,1]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,2]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,2]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,2,1]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,2,1]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,1,1]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,2]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,2,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1,1]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,1]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1,1,1]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,1,1]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,2]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,2,1]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,1,1]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2,1]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1]
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1,1]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1,1]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1,1]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1,1]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1,1]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,1]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,1]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,1]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1,1,1]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1,1,1]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1,1,1]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1,1]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1,1]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1,1]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1,1,1]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1,1]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1,1,1]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,1,1]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,1,1]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,1,1]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,1]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,2]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,2]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,2]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,2]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,2]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,2,1]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,2,1]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,2,1]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,2,1]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,2,1]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,1]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,1]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,1,1]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,1,1]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,2]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,2]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,2,1]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,2,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1,1]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,1]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1,1,1]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,1,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,2]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,2,1]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,1]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,1,1]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1,1]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1,1]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,1,1]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,1]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,2]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2,1]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,2,1]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,1,1]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,2]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,2,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1,1]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,2]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,2,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
searching the database
Sorry, this map was not found in the database.