Identifier
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-1
[.,.]=>[1,0]=>[1]=>[1]
[.,[.,.]]=>[1,0,1,0]=>[1,1]=>[2]
[[.,.],.]=>[1,1,0,0]=>[2]=>[1,1]
[.,[.,[.,.]]]=>[1,0,1,0,1,0]=>[1,1,1]=>[3]
[.,[[.,.],.]]=>[1,0,1,1,0,0]=>[1,2]=>[2,1]
[[.,.],[.,.]]=>[1,1,0,0,1,0]=>[2,1]=>[1,2]
[[.,[.,.]],.]=>[1,1,0,1,0,0]=>[2,1]=>[1,2]
[[[.,.],.],.]=>[1,1,1,0,0,0]=>[3]=>[1,1,1]
[.,[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>[4]
[.,[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0]=>[1,1,2]=>[3,1]
[.,[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0]=>[1,2,1]=>[2,2]
[.,[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0]=>[1,2,1]=>[2,2]
[.,[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0]=>[1,3]=>[2,1,1]
[[.,.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0]=>[2,1,1]=>[1,3]
[[.,.],[[.,.],.]]=>[1,1,0,0,1,1,0,0]=>[2,2]=>[1,2,1]
[[.,[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0]=>[2,1,1]=>[1,3]
[[[.,.],.],[.,.]]=>[1,1,1,0,0,0,1,0]=>[3,1]=>[1,1,2]
[[.,[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0]=>[2,1,1]=>[1,3]
[[.,[[.,.],.]],.]=>[1,1,0,1,1,0,0,0]=>[2,2]=>[1,2,1]
[[[.,.],[.,.]],.]=>[1,1,1,0,0,1,0,0]=>[3,1]=>[1,1,2]
[[[.,[.,.]],.],.]=>[1,1,1,0,1,0,0,0]=>[3,1]=>[1,1,2]
[[[[.,.],.],.],.]=>[1,1,1,1,0,0,0,0]=>[4]=>[1,1,1,1]
[.,[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]=>[5]
[.,[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>[4,1]
[.,[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>[3,2]
[.,[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>[3,2]
[.,[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>[2,3]
[.,[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>[2,3]
[.,[[[.,.],.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>[2,1,2]
[.,[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>[2,3]
[.,[[.,[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]=>[2,2,1]
[.,[[[.,.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>[2,1,2]
[.,[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>[2,1,2]
[.,[[[[.,.],.],.],.]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>[2,1,1,1]
[[.,.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>[1,4]
[[.,.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>[1,3,1]
[[.,.],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>[1,2,2]
[[.,.],[[[.,.],.],.]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>[1,2,1,1]
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>[1,4]
[[.,[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]=>[1,3,1]
[[[.,.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>[1,1,3]
[[[.,.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>[1,1,2,1]
[[.,[.,[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>[1,4]
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>[1,2,2]
[[[.,.],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>[1,1,3]
[[[.,[.,.]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>[1,1,3]
[[[[.,.],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>[1,1,1,2]
[[.,[.,[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>[1,4]
[[.,[.,[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]=>[1,3,1]
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>[1,2,2]
[[.,[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>[1,2,2]
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3]=>[1,2,1,1]
[[[.,.],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>[1,1,3]
[[[.,.],[[.,.],.]],.]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2]=>[1,1,2,1]
[[[.,[.,.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>[1,1,3]
[[[[.,.],.],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>[1,1,1,2]
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>[1,1,3]
[[[.,[[.,.],.]],.],.]=>[1,1,1,0,1,1,0,0,0,0]=>[3,2]=>[1,1,2,1]
[[[[.,.],[.,.]],.],.]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>[1,1,1,2]
[[[[.,[.,.]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>[1,1,1,2]
[[[[[.,.],.],.],.],.]=>[1,1,1,1,1,0,0,0,0,0]=>[5]=>[1,1,1,1,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>[6]
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>[5,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>[4,2]
[.,[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>[4,2]
[.,[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>[4,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>[3,3]
[.,[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>[3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>[3,3]
[.,[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>[3,1,2]
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>[3,3]
[.,[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]=>[3,2,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>[3,1,2]
[.,[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>[3,1,2]
[.,[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>[3,1,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>[2,4]
[.,[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>[2,3,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>[2,2,2]
[.,[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>[2,2,2]
[.,[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>[2,2,1,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>[2,4]
[.,[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]=>[2,3,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>[2,1,3]
[.,[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>[2,1,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>[2,4]
[.,[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>[2,2,2]
[.,[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>[2,1,3]
[.,[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>[2,1,3]
[.,[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>[2,1,1,2]
[.,[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>[2,4]
[.,[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]=>[2,3,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>[2,2,2]
[.,[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>[2,2,2]
[.,[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]=>[2,2,1,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>[2,1,3]
[.,[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]=>[2,1,2,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>[2,1,3]
[.,[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>[2,1,1,2]
[.,[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>[2,1,3]
[.,[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]=>[2,1,2,1]
[.,[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>[2,1,1,2]
[.,[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>[2,1,1,2]
[.,[[[[[.,.],.],.],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>[2,1,1,1,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,5]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>[1,4,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,3,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,3,2]
[[.,.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>[1,3,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>[1,2,3]
[[.,.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>[1,2,2,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]=>[1,2,3]
[[.,.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>[1,2,1,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>[1,2,3]
[[.,.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]=>[1,2,2,1]
[[.,.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>[1,2,1,2]
[[.,.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>[1,2,1,2]
[[.,.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>[1,2,1,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,5]
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]=>[1,4,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,3,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,3,2]
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]=>[1,3,1,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[1,1,4]
[[[.,.],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>[1,1,3,1]
[[[.,.],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>[1,1,2,2]
[[[.,.],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>[1,1,2,2]
[[[.,.],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>[1,1,2,1,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]=>[1,5]
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]=>[1,4,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>[1,2,3]
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]=>[1,2,2,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,4]
[[[.,.],[.,.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]=>[1,1,3,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,4]
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]=>[1,1,3,1]
[[[[.,.],.],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>[1,1,1,3]
[[[[.,.],.],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>[1,1,1,2,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]=>[1,5]
[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>[1,3,2]
[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>[1,2,3]
[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>[1,2,3]
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>[1,2,1,2]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,4]
[[[.,.],[[.,.],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>[1,1,2,2]
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,4]
[[[[.,.],.],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>[1,1,1,3]
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>[1,1,4]
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>[1,1,2,2]
[[[[.,.],[.,.]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>[1,1,1,3]
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>[1,1,1,3]
[[[[[.,.],.],.],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>[1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]=>[1,5]
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]=>[1,4,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>[1,3,2]
[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>[1,3,2]
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]=>[1,3,1,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>[1,2,3]
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]=>[1,2,2,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>[1,2,3]
[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>[1,2,1,2]
[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>[1,2,3]
[[.,[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]=>[1,2,2,1]
[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>[1,2,1,2]
[[.,[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>[1,2,1,2]
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]=>[1,2,1,1,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,4]
[[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]=>[1,1,3,1]
[[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>[1,1,2,2]
[[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>[1,1,2,2]
[[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]=>[1,1,2,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,4]
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]=>[1,1,3,1]
[[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>[1,1,1,3]
[[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]=>[1,1,1,2,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>[1,1,4]
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>[1,1,2,2]
[[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>[1,1,1,3]
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1,1,3]
[[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>[1,1,1,1,2]
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>[1,1,4]
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]=>[1,1,3,1]
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>[1,1,2,2]
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>[1,1,2,2]
[[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]=>[1,1,2,1,1]
[[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>[1,1,1,3]
[[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]=>[1,1,1,2,1]
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>[1,1,1,3]
[[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>[1,1,1,1,2]
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>[1,1,1,3]
[[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]=>[1,1,1,2,1]
[[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>[1,1,1,1,2]
[[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>[1,1,1,1,2]
[[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]=>[7]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]=>[6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>[5,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]=>[5,2]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>[5,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>[4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>[4,2,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]=>[4,3]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>[4,1,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]=>[4,3]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]=>[4,2,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>[4,1,2]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>[4,1,2]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>[4,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>[3,4]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>[3,3,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>[3,2,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>[3,2,2]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]=>[3,4]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]=>[3,3,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>[3,1,3]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>[3,1,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]=>[3,4]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>[3,2,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>[3,1,3]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>[3,1,3]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>[3,1,1,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]=>[3,4]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]=>[3,3,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>[3,2,2]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>[3,2,2]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]=>[3,2,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>[3,1,3]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]=>[3,1,2,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>[3,1,3]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>[3,1,1,2]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>[3,1,3]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]=>[3,1,2,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>[3,1,1,2]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>[3,1,1,2]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>[3,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[2,5]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,4,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[2,3,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[2,3,2]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>[2,3,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>[2,2,1,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>[2,2,1,2]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>[2,2,1,2]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>[2,2,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[2,5]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,4,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[2,3,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[2,3,2]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]=>[2,3,1,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>[2,1,2,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]=>[2,5]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]=>[2,4,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>[2,1,1,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]=>[2,5]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>[2,3,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>[2,2,1,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>[2,1,1,1,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]=>[2,5]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]=>[2,4,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>[2,3,2]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>[2,3,2]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]=>[2,3,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>[2,2,1,2]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>[2,2,3]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]=>[2,2,2,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>[2,2,1,2]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>[2,2,1,2]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]=>[2,2,1,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]=>[2,1,2,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]=>[2,1,1,2,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>[2,1,1,1,2]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>[2,1,4]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]=>[2,1,3,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>[2,1,2,2]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]=>[2,1,2,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]=>[2,1,1,2,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>[2,1,1,1,2]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>[2,1,1,3]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]=>[2,1,1,2,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>[2,1,1,1,2]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>[2,1,1,1,2]
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>[2,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[1,4,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[1,3,2,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[1,3,2,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[1,3,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>[1,2,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>[1,2,1,2,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]=>[1,2,2,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]=>[1,2,1,2,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]=>[1,2,1,2,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>[1,2,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[1,4,1,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[1,3,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[1,3,2,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[1,3,1,1,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,3,1,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[1,1,2,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]=>[1,4,1,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]=>[1,2,2,1,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,3,1,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,3,1,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>[1,1,1,2,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]=>[1,3,2,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]=>[1,2,1,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>[1,1,1,1,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]=>[1,6]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>[1,2,1,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>[1,1,2,1,2]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>[1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]=>[1,6]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]=>[1,5,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>[1,4,2]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]=>[1,4,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]=>[1,3,2,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>[1,3,3]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]=>[1,3,2,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]=>[1,3,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]=>[1,2,2,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]=>[1,2,1,2,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>[1,2,4]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]=>[1,2,3,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]=>[1,2,2,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]=>[1,2,1,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>[1,2,1,3]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]=>[1,2,1,2,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>[1,2,1,1,2]
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]=>[1,2,1,1,1,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]=>[1,1,3,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]=>[1,1,2,1,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]=>[1,1,3,1,1]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]=>[1,1,1,2,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]=>[1,1,1,1,2,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1,1,1,1,1,2]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,5]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]=>[1,1,4,1]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>[1,1,3,2]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]=>[1,1,3,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]=>[1,1,2,2,1]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>[1,1,2,1,2]
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]=>[1,1,2,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]=>[1,1,1,2,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]=>[1,1,1,1,2,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>[1,1,1,1,1,2]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]=>[1,1,1,3,1]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>[1,1,1,2,2]
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]=>[1,1,1,2,1,1]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]=>[1,1,1,1,2,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>[1,1,1,1,1,2]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]=>[1,1,1,1,3]
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]=>[1,1,1,1,2,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>[1,1,1,1,1,2]
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>[1,1,1,1,1,2]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]=>[8]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]=>[7,1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>[6,2]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]=>[6,2]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>[6,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>[5,3]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>[5,2,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]=>[5,3]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>[5,1,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]=>[5,3]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]=>[5,2,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]=>[5,1,2]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]=>[5,1,2]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>[5,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[4,4]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>[4,3,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>[4,2,2]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]=>[4,2,2]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>[4,2,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[4,4]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]=>[4,3,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>[4,1,3]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>[4,1,2,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]=>[4,4]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]=>[4,2,2]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]=>[4,1,3]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]=>[4,1,3]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>[4,1,1,2]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]=>[4,4]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]=>[4,3,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]=>[4,2,2]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]=>[4,2,2]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]=>[4,2,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]=>[4,1,3]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]=>[4,1,2,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]=>[4,1,3]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]=>[4,1,1,2]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]=>[4,1,3]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]=>[4,1,2,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]=>[4,1,1,2]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]=>[4,1,1,2]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>[4,1,1,1,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[3,4,1]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[3,3,2]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>[3,3,2]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[3,3,1,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>[3,2,2,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>[3,2,1,2]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]=>[3,2,2,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]=>[3,2,1,2]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]=>[3,2,1,2]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>[3,2,1,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[3,4,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[3,3,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>[3,3,2]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[3,3,1,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>[3,1,3,1]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[3,1,2,1,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]=>[3,4,1]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]=>[3,2,2,1]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]=>[3,1,3,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]=>[3,1,3,1]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>[3,1,1,2,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]=>[3,3,2]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]=>[3,2,1,2]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>[3,1,1,1,2]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]=>[3,5]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]=>[3,4,1]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]=>[3,3,2]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]=>[3,3,2]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]=>[3,3,1,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]=>[3,2,2,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]=>[3,2,1,2]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]=>[3,2,3]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]=>[3,2,2,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]=>[3,2,1,2]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]=>[3,2,1,2]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]=>[3,2,1,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]=>[3,1,3,1]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]=>[3,1,2,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]=>[3,1,3,1]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]=>[3,1,1,2,1]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]=>[3,1,1,1,2]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]=>[3,1,4]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]=>[3,1,3,1]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]=>[3,1,2,2]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]=>[3,1,2,1,1]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]=>[3,1,1,2,1]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]=>[3,1,1,1,2]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]=>[3,1,1,3]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]=>[3,1,1,2,1]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]=>[3,1,1,1,2]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]=>[3,1,1,1,2]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>[3,1,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,3,2,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[2,3,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,2,1,2,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>[2,2,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,3,2,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[2,3,1,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[2,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,3,2,1]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,2,1,2,1]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>[2,1,1,1,2,1]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>[2,1,1,1,1,2]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]=>[2,6]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]=>[2,5,1]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]=>[2,4,2]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]=>[2,3,3]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]=>[2,3,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]=>[2,2,4]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]=>[2,2,1,1,1,1]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]=>[2,1,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]=>[2,1,1,1,1,2]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]=>[2,1,5]
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]=>[2,1,2,1,1,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[1,3,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>[1,2,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[1,3,1,1,1,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[1,1,2,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1,1,1,1,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]=>[1,7]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]=>[1,6,1]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]=>[1,5,2]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]=>[1,4,3]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]=>[1,3,4]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]=>[1,3,1,1,1,1]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]=>[1,2,5]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]=>[1,2,1,1,1,1,1]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]=>[1,1,2,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1,1,1,1,1,1,2]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]=>[1,1,6]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]=>[1,1,2,1,1,1,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>[1,1,1,1,1,1,1,1]
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
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