- FindStat

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Identifier

Mp00141: Binary trees —pruning number to logarithmic height⟶ Dyck paths

Images

=>
            
              Cc0010;cc-rep-0Cc0005;cc-rep-1
            

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[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
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[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
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[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
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[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
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[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
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[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
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[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
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[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
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[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
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[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
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[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
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[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
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[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
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[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
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[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
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[[[[.,.],.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
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[[[[.,.],[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
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[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
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[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
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[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,[[.,.],[[.,[[.,.],.]],.]]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[.,[[.,[.,.]],[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[.,[[.,.],[[.,[[[.,.],.],[.,.]]],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],[[.,[[.,.],.]],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[.,[.,.]],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,[[[[[[.,.],[.,.]],.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
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[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[.,.],[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[.,.],[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[[.,.],.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[.,[[.,.],.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[.,[[[.,.],.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[.,.],[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[[.,[[.,[[.,.],.]],.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[.,[[.,[.,.]],[.,.]]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[[[.,.],[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
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[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
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[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
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[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
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[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
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[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[.,[[.,.],[[.,[.,.]],.]]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0]
[[.,[[.,.],[[[.,[.,.]],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]
[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,[[.,.],[[.,[.,.]],.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[.,[.,[[[.,[.,.]],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[[[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[[[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]
[[[[[.,[[.,[.,[.,.]]],.]],[.,.]],.],.],.]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[.,[[[.,.],[.,.]],.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,[[[.,.],[[.,.],[.,.]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,[[[.,.],[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,[[[.,.],[.,.]],.]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[.,.],[[.,[[[.,.],[.,.]],.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[.,[[.,[[[[.,.],[.,.]],[[.,.],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[[[.,.],[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[[.,.],[.,.]],[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[[.,.],[.,.]],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,.],[.,[[.,[[[.,.],[[.,.],.]],.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[.,[[[.,.],[[.,.],[[.,.],.]]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[.,[[[.,.],[[.,.],.]],.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[.,[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]
[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]],.]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]
[[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[[.,.],[[[[.,[[.,.],.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[.,.],[[[.,[[.,.],[[.,.],.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,[[.,.],.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[[.,.],.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[[[.,.],[[.,.],[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[[.,[[.,.],.]],.],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],[[.,.],.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[.,.],[[[[.,[[.,.],.]],[.,.]],.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[.,.],[[[.,[[.,.],[[.,.],.]]],.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,1,1,0,0]
[.,[[.,.],[[.,.],[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],[[.,.],.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[.,[[.,.],[[[.,[[.,.],.]],.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[.,[.,[.,[[.,.],[[.,[[[.,.],.],.]],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[.,[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]
[.,[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]
[.,[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]
[.,[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]
[.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]
[[[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]],.],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[.,.],[[.,[.,[.,[.,.]]]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[[.,.],[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,0]
[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0]
[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[.,[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[.,[[.,.],[[[[.,.],[[.,.],.]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[.,[.,[[[[.,.],[[.,.],.]],[.,.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[.,[[.,.],[[[.,.],[[.,[[.,.],.]],.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[.,[[[[[.,.],[[.,[.,.]],.]],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[.,[[.,[.,.]],.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[.,[[.,.],[[[.,.],[[.,.],.]],.]]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,[.,[[[.,.],[[.,[[.,.],.]],.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[[.,[.,[[[.,.],[[.,.],.]],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0,0]
[[[[.,[[.,[.,[.,.]]],.]],[[.,.],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,1,0,0]
[.,[[[[.,[[.,[.,.]],.]],[[.,.],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0]
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
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[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
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[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.]=>[1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]
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[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[.,[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[.,[.,.]],[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[.,[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]]=>[1,1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,1,1,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0]
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0,0]
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[.,.],[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,.],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[.,.],[[[.,[[.,.],[[.,[.,.]],.]]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[.,[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[.,.],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[.,[[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0]
[.,[[[.,[[.,.],[[[.,[.,.]],[.,.]],.]]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[[[[.,[[.,.],[[.,[.,.]],.]]],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[[.,[.,.]],[[.,.],[[.,[.,.]],.]]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,[[[.,[[.,.],[[.,[.,.]],.]]],[.,.]],.]],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[.,.],[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[.,[[.,.],[[[.,[.,.]],[.,.]],.]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]
[[.,.],[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,.]],[[.,.],[[.,.],[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[.,[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,.]],[[.,.],[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[[.,.],[[.,[.,.]],.]]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[[[.,[.,.]],.],[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[.,[.,.]],.],[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[.,[[.,[.,.]],.]],.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[[.,.],[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,[[.,.],[[.,[.,.]],.]]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,[[[.,[.,.]],[.,.]],.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,[[.,[.,.]],.]]],.],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[[[[.,[.,.]],[.,[[.,[.,.]],.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0]
[[[.,[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]
[[[.,.],[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[[[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,[[.,.],[[.,[.,.]],.]]]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[[[.,[.,[[[.,[.,.]],[.,.]],.]]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[.,[.,[[.,.],[[.,[.,.]],.]]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[.,[.,[[[.,[.,.]],[.,.]],.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[.,[.,[[.,[.,.]],.]]],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[[.,[[.,[.,.]],.]],[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[.,[.,[[.,[.,.]],.]]],[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,0]
[[[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[.,[.,.]],[.,[[.,.],[[.,[.,.]],.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[.,[.,.]],[.,[[[.,[.,.]],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[[.,[.,.]],[.,[[.,[.,.]],.]]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[[.,[.,.]],[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0]
[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0,0]
[[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[[.,[[[.,.],[.,.]],.]],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[[.,.],[.,.]]],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]]],.]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,[[[.,.],[.,.]],.]]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,.],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],[[.,.],.]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,[[.,[[[.,.],[.,.]],.]],.]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[[[.,[[[.,.],[[.,.],[.,.]]],.]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,[[[.,.],[.,.]],.]]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[.,[[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[.,[[.,[[[.,.],[.,.]],.]],.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[[[.,.],[[.,.],[.,.]]],.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[.,[[.,[[[.,[[[.,.],[.,.]],.]],[[.,.],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[.,[[[.,.],[[.,[[[.,.],[.,.]],.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[.,[[[.,.],[.,.]],.]],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[.,[[[.,.],[.,.]],.]],[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[.,.],[[.,.],[[.,[[[.,.],[.,.]],.]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[.,[[.,[[.,[[[[.,.],[.,.]],[[.,.],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[[.,.],[[[.,.],[.,.]],[[.,.],.]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[.,[[[[.,.],[.,.]],[[.,.],.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],.]],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[[.,.],.]],.]]]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,[[[[.,.],[.,.]],[[.,.],.]],.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[.,.],[[[.,.],[.,.]],[[.,.],.]]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[.,[[[[.,.],[.,.]],[[.,.],.]],.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[.,[[[[[.,.],[.,.]],.],[[.,.],[.,.]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,[[[.,.],[.,.]],.]],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],.],[[.,.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[.,[[[.,.],[.,[[.,[[[.,.],[[.,.],.]],.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[[.,.],[.,[[[.,.],[[.,.],[[.,.],.]]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],[.,[[[.,.],[[.,.],.]],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[[.,[[.,[[[.,.],[.,.]],.]],.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],.],[[.,.],[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,[[[.,.],[.,.]],.]]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,.],[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[.,[[[[[.,.],[.,.]],.],[[.,.],[.,.]]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[.,[[[.,.],[.,.]],.]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,.],[[.,.],[.,[[.,[[[.,.],[[.,.],.]],.]],.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[[.,.],[.,[[[.,.],[[.,.],[[.,.],.]]],.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[.,[[[.,.],[[.,.],.]],.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[.,[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[.,[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[.,[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[.,[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[.,[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0]
[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0]
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[.,[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],[[[.,.],[.,.]],[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],[.,[[.,.],[[.,[[.,.],.]],.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[.,[[.,.],.]],[.,[[.,[[.,.],[[.,.],.]]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[[.,[[.,.],[[.,.],.]]],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0]
[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[[.,.],[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,.],[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[.,.],[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,.],[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[.,.],[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[.,.],[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[.,.],[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0]
[[[.,.],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0]
[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0]
[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[[.,.],.]]]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0]
[[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]
[[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[[[[.,[[.,.],.]],[.,.]],[.,.]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[.,[[.,.],[[[.,[[.,.],[[.,.],.]]],[.,.]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,[[.,.],.]],[.,[[.,.],.]]],.]]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],[.,.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,[[.,.],[[.,.],[[[.,[[.,.],.]],[.,.]],.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0]
[[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],[[[.,[[.,.],.]],[.,.]],[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]
[[.,.],[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]
[[.,.],[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[[.,.],[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[.,.],[[[.,[[.,.],[[.,.],.]]],[.,.]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[.,.],[[[.,[[.,.],.]],[.,[[.,.],.]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,0]
[[.,.],[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,.],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[[[.,[[.,.],.]],[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],.]],[[[.,[[.,.],.]],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]
[[[[[.,.],[[.,[[.,.],.]],.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[.,.],[[.,[[.,.],.]],.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0]
[[[[.,.],[[.,[[.,.],.]],.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0]
[[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[[[[.,.],[[.,.],[[.,.],.]]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[[.,[[.,.],[[[.,[[.,.],.]],.],.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[[.,.],[[.,.],.]],[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[[[.,[[.,.],.]],[.,.]],.],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[.,[[.,.],[[[.,[[.,.],[[.,.],.]]],.],.]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],.],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[[[.,[[.,.],.]],.],.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[[.,.],[[.,.],.]],[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,0]
[[[[.,.],[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[[.,[[.,.],.]],.],[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[.,.],[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[.,.],[[[[[.,[[.,.],.]],[.,.]],[.,.]],.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[[.,.],[[[[.,[[.,.],[[.,.],.]]],[.,.]],.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[[.,[[.,.],.]],.],.]]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,1,0,0]
[.,[[.,.],[[[[.,[[.,.],.]],[.,[[.,.],.]]],.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[.,[[.,.],[[[.,[[.,.],[[.,.],[[.,.],.]]]],.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[.,[[[[.,[[.,.],.]],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[[.,[[.,.],[[.,.],.]]],.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[[[[.,[[.,.],.]],[.,.]],.],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[.,.],[[.,.],[[[.,[[.,.],[[.,.],.]]],.],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,0]
[.,[[.,.],[[[.,[[.,.],.]],.],[[.,[[.,.],.]],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],[[[.,[[.,.],.]],.],.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[.,[[.,.],[[.,.],[[.,.],[[[.,[[.,.],.]],.],.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[[[.,.],[[.,.],[[.,.],.]]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[[.,[[.,.],.]],.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],[[.,.],.]],[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,[[.,.],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[.,.],[[[[.,[[.,.],.]],[.,.]],.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0]
[.,[[.,.],[[[.,[[.,.],[[.,.],.]]],.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[.,.],[[[.,[[.,.],.]],.],[[.,.],.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[.,.],[[.,.],.]],[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0,1,0,0]
[.,[[.,.],[[[.,[[.,.],.]],.],[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0]
[.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[[[.,.],[[.,[.,.]],.]],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,.],[[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[.,.],[[[.,.],[[.,[.,.]],.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,0]
[[.,.],[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[.,.],[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]
[[.,.],[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[.,.],[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0]
[[[[.,.],[[.,[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,0]
[[[[.,.],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[[[.,.],[.,[[[.,.],[.,.]],.]]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,[[[.,.],[.,.]],.]]],[[.,[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,[[.,[.,.]],.]],.]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0,0,0]
[[[[.,.],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,1,0,0,1,0]
[[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[.,.],[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[[.,[[.,[.,.]],.]],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,[.,[[[.,.],[.,.]],.]]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[[.,.],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,.],[[.,[.,[[.,.],[[[.,.],[.,.]],.]]]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,[.,[[[.,.],[[.,[.,.]],.]],.]]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,.],[[.,[[.,[.,[[[.,.],[.,.]],.]]],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,[[.,.],.]],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,[[.,.],.]],[[[[.,.],[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[.,.],.]],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[[.,.],.]],[[.,[.,.]],.]],[[[.,.],[.,.]],.]]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0,0]
[[[[.,[[.,.],.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0,1,0]
[[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[[.,.],.]],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[.,[[.,.],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[[.,.],[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,0]
[.,[[[.,.],[[.,.],.]],[[[.,.],[[.,[.,.]],.]],.]]]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,1,0]
[[[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[.,[[[[.,.],[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[.,[[[[.,.],[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],[[[.,.],[.,.]],.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[.,[[.,[[.,.],.]],[[[.,.],[[.,[.,.]],.]],.]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[.,[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[[.,.],.]],[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[.,[[.,.],[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[.,[[[.,.],[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[.,[[[.,.],[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,[[[.,[[.,.],.]],[.,.]],.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]
[[[.,[[[.,[[.,.],.]],[.,.]],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],[[.,.],.]],[[[.,.],[.,.]],.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[[.,[.,[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[.,[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[.,[[.,.],[[.,.],[[[[.,.],[[.,.],.]],[.,.]],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[[.,.],[.,[[[[.,.],[[.,.],.]],[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,.],[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0]
[[[.,[.,[[[[.,.],[[.,.],.]],[.,.]],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[.,[.,[[.,.],[[[[.,.],[[.,.],.]],[.,.]],.]]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,[.,[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[.,[[.,[.,[[[[.,.],[[.,.],.]],[.,.]],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[[[.,.],[[.,[[.,.],.]],.]],.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[.,[[.,.],[[[[[.,.],[[.,[.,.]],.]],.],[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[.,[[.,.],[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[.,[[[[.,.],[[.,[.,.]],.]],.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,0]
[.,[[[[[.,.],[[.,[.,.]],.]],.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[.,[[[[[.,.],[.,[[[.,.],[.,.]],.]]],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[.,[[[[[.,.],[[.,[[.,[.,.]],.]],.]],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[[.,.],[[[.,.],[[.,.],.]],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[.,[[[.,.],[.,[[[.,.],[[.,[[.,.],.]],.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[.,[[[.,.],[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[[.,.],[[.,[.,[[[.,.],[[.,.],.]],.]]],.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[.,[[[[[.,[[.,.],.]],[[.,[.,.]],.]],.],[.,.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0]
[[[[.,[[.,[.,.]],.]],.],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[.,[[.,[.,.]],.]],.],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[.,[[[.,.],[.,.]],.]]],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[.,[.,[[[.,.],[.,.]],.]]],.],[[.,[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[.,[.,[[.,.],[[[.,.],[.,.]],.]]]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[[[.,[.,[[[.,.],[[.,[.,.]],.]],.]]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0]
[[[[.,[[.,[.,[[[.,.],[.,.]],.]]],.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],[.,.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,[.,[[.,.],[[[.,.],[[.,[[.,.],.]],.]],.]]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[.,[[[[[.,.],[[.,[.,.]],.]],.],[.,.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[.,[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,[[.,[.,.]],.]],.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[.,[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[.,[[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[[.,[.,[[.,.],[[[.,.],[[.,.],.]],.]]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,[.,[[[.,.],[[.,[[.,.],.]],.]],.]]],.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[[.,[[.,[.,[[[.,.],[[.,.],.]],.]]],.]],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
          

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

Francon's map from binary trees to Dyck paths.
This bijection sends the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree., to the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path.. The implementation is a literal translation of Knuth's [2].

References

[1] Françon, J. Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique MathSciNet:0775838
[2] http://www-cs-faculty.stanford.edu/~knuth/programs/francon.w

Properties

bijective, graded

Sage code

def mapping(B):
    def binary_tree_to_LR(B, largest=0):
        if not B[0].is_empty():
            left_link = largest+1
            left = binary_tree_to_LR(B[0], largest=largest+1)
            largest = max(max(max(a,b) for a,b in left), largest+1)
        else:
            left_link = 0
            left = []

        if not B[1].is_empty():
            right_link = largest+1
            right = binary_tree_to_LR(B[1], largest=largest+1)
        else:
            right_link = 0
            right = []

        return [(left_link, right_link)] + left + right

    links = binary_tree_to_LR(B)
    l = [0] + [e for e, _ in links]
    r = [0] + [e for _, e in links]
    n = B.node_number()
    d = [1]*(2*n+1)
    h = [0]*(2*n+3)
    q = [0]*(n+1)
    qm = [0]*(n+1)

    h[1] = 1; k = 2; p = 0
    while True:
        while h[k] != 0:
            k += 2
        kk = h[k//2]
        if l[kk] != 0:
            h[k] = l[kk]+1; p += 1; d[p] = 1
        else:
            p += 1; d[p] = 0
        if r[kk] != 0:
            h[k+1] = r[kk]+1; p += 1; d[p] = 1
        else:
            p += 1; d[p] = 0
        if h[k] != 0:
            if h[k+1] != 0:
                continue
            kk = k
        elif h[k+1] != 0:
            kk = k+1
        else:
            h[k//2] = 0; kk = (k//2) ^^ 1; k = kk & -2
            if k == 0:
                return DyckWord(d[:-1])
        j = 0; jj = 1; q[0] = kk; qm[0] = 1
        while j < jj:
            kk = q[j]
            h[((kk//2)&(-qm[j]))+(kk&(qm[j]-1))] = h[kk]
            if h[2*kk] != 0:
                q[jj] = 2*kk;
                q[jj+1] = 2*kk+1
                qm[jj] = qm[jj+1] = qm[j]*2
                jj = jj + 2
            else:
                h[kk] = 0
            j += 1

Weight

Created

Jan 31, 2020 at 19:19 by FindStatCrew

Updated

Jan 31, 2020 at 19:19 by Martin Rubey