Identifier
Mp00011: Binary trees —to graph⟶ Graphs
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0Cc0020;cc-rep-1
[.,.]=>([],1)=>[1]=>[1] [.,[.,.]]=>([(0,1)],2)=>[1,1]=>[1,1] [[.,.],.]=>([(0,1)],2)=>[1,1]=>[1,1] [.,[.,[.,.]]]=>([(0,2),(1,2)],3)=>[2,1]=>[2,1] [.,[[.,.],.]]=>([(0,2),(1,2)],3)=>[2,1]=>[2,1] [[.,.],[.,.]]=>([(0,2),(1,2)],3)=>[2,1]=>[2,1] [[.,[.,.]],.]=>([(0,2),(1,2)],3)=>[2,1]=>[2,1] [[[.,.],.],.]=>([(0,2),(1,2)],3)=>[2,1]=>[2,1] [.,[.,[.,[.,.]]]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [.,[.,[[.,.],.]]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [.,[[.,.],[.,.]]]=>([(0,3),(1,3),(2,3)],4)=>[3,1]=>[3,1] [.,[[.,[.,.]],.]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [.,[[[.,.],.],.]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[.,.],[.,[.,.]]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[.,.],[[.,.],.]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[.,[.,.]],[.,.]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[[.,.],.],[.,.]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[.,[.,[.,.]]],.]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[.,[[.,.],.]],.]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[[.,.],[.,.]],.]=>([(0,3),(1,3),(2,3)],4)=>[3,1]=>[3,1] [[[.,[.,.]],.],.]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[[[.,.],.],.],.]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [.,[.,[.,[.,[.,.]]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[.,[.,[[.,.],.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[.,[[.,.],[.,.]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [.,[.,[[.,[.,.]],.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[.,[[[.,.],.],.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[[.,.],[.,[.,.]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [.,[[.,.],[[.,.],.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [.,[[.,[.,.]],[.,.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [.,[[[.,.],.],[.,.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [.,[[.,[.,[.,.]]],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[[.,[[.,.],.]],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[[[.,.],[.,.]],.]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [.,[[[.,[.,.]],.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[[[[.,.],.],.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,.],[.,[.,[.,.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,.],[.,[[.,.],.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,.],[[.,.],[.,.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[.,.],[[.,[.,.]],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,.],[[[.,.],.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[.,.]],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[.,.]],[[.,.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[.,.],.],[[.,.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[.,[.,.]]],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[[.,.],.]],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[.,.],[.,.]],[.,.]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[[.,[.,.]],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[[.,.],.],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[.,[.,[.,.]]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[.,[[.,.],.]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[[.,.],[.,.]]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[.,[[.,[.,.]],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[.,[[[.,.],.],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[.,.],[.,[.,.]]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[[.,.],[[.,.],.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[[.,[.,.]],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[[[.,.],.],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[.,[[.,.],.]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[[.,.],[.,.]],.],.]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[3,2] [[[[.,[.,.]],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [[[[[.,.],.],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[3,2] [.,[.,[.,[.,[.,[.,.]]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[.,[.,[[.,.],.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[.,[[.,.],[.,.]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[.,[.,[[.,[.,.]],.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[.,[[[.,.],.],.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[[.,.],[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[.,[[.,.],[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[.,[[.,[.,.]],[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[.,[[[.,.],.],[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[.,[[.,[.,[.,.]]],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[[.,[[.,.],.]],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[[[.,.],[.,.]],.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[.,[[[.,[.,.]],.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[[[[.,.],.],.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[.,.],[.,[.,[.,.]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,.],[.,[[.,.],.]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,.],[[.,.],[.,.]]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,.],[[.,[.,.]],.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,.],[[[.,.],.],.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,[.,.]],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[.,[.,.]],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[[.,.],.],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[[.,.],.],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[.,[.,[.,.]]],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,[[.,.],.]],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[[.,.],[.,.]],[.,.]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[[.,[.,.]],.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[[[.,.],.],.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,[.,[.,[.,.]]]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[.,[.,[[.,.],.]]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[.,[[.,.],[.,.]]],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[.,[[.,[.,.]],.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[.,[[[.,.],.],.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[[.,.],[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[[.,.],[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[[.,[.,.]],[.,.]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[[[.,.],.],[.,.]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [.,[[[.,[.,[.,.]]],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[[.,[[.,.],.]],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[[[.,.],[.,.]],.],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [.,[[[[.,[.,.]],.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[[[[[.,.],.],.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[.,[.,[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[.,[.,[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[.,[[.,.],[.,.]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[.,.],[.,[[.,[.,.]],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[.,[[[.,.],.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[[.,.],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,.],[[.,.],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,.],[[.,[.,.]],[.,.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,.],[[[.,.],.],[.,.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,.],[[.,[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[[.,[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[[[.,.],[.,.]],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[.,.],[[[.,[.,.]],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,.],[[[[.,.],.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,.]],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,.]],[.,[[.,.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,.]],[[.,.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[.,[.,.]],[[.,[.,.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,.]],[[[.,.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,.],.],[.,[[.,.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,.],.],[[.,.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,.],.],[[.,[.,.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,.],.],[[[.,.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[.,.]]],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[.,.]]],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[.,.],.]],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[.,.],.]],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,.],[.,.]],[[.,.],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,[.,.]],.],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[.,.],.],.],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[.,[.,.]]]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[[.,.],.]]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[.,.],[.,.]]],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[.,[[.,[.,.]],.]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[[.,.],.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[.,.],[[.,.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[.,[.,.]],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[.,[.,[.,.]]],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,[[.,.],.]],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[[.,[.,.]],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[[.,.],.],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[.,[[.,.],.]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[[.,.],[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[.,[.,[[.,[.,.]],.]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[.,[[[.,.],.],.]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[.,.],[.,[.,.]]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,[[.,.],[[.,.],.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,[[.,[.,.]],[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,[[[.,.],.],[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[[.,.],[.,.]],.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[.,[[[.,[.,.]],.],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[.,[[[[.,.],.],.],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,.],[.,[.,[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,.],[.,[[.,.],.]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,.],[[.,.],[.,.]]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,.],[[.,[.,.]],.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,.],[[[.,.],.],.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,[.,.]],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[.,[.,.]],[[.,.],.]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[.,.],.],[[.,.],.]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[.,[.,[.,.]]],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,[[.,.],.]],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[[.,.],[.,.]],[.,.]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[[.,[.,.]],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[[[.,.],.],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,[.,[[.,.],.]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,[[.,.],[.,.]]],.],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[.,[[[.,.],.],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[.,.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[.,.],[[.,.],.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[.,[.,.]],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[[.,.],.],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[[.,.],[.,.]],.],.],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[4,2] [[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[[[[.,.],.],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[.,[[[[.,.],.],.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,.],[[[.,.],.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,.],.],[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[[.,.],.],.],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[.,[[[.,.],.],.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,.],[[.,.],.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[[.,.],.],[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,[.,[.,.]]],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[[.,[[.,.],.]],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[[[.,.],[.,.]],.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[[[.,[.,.]],.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[.,[[[[[.,.],.],.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[.,[.,[[.,.],.]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[.,[[.,.],[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [.,[[.,.],[.,[[.,[.,.]],.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[.,[[[.,.],.],.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[.,.],[.,[.,.]]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[.,.],[[.,.],.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[[.,.],.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[.,[[.,.],.]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[[.,.],[.,.]],.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [.,[[.,.],[[[.,[.,.]],.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,.],[[[[.,.],.],.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,.]],[.,[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,.]],[[.,.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,.]],[[.,[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,.]],[[[.,.],.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],.],[.,[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],.],[.,[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],.],[[.,.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],.],[[.,[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],.],[[[.,.],.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[.,.]]],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,.],.]],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,.],.]],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[.,.]],[.,[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[.,.]],[[.,.],.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,.]],.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,.]],.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],.],.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],.],.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[[.,.],.]]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,.],[.,.]]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [.,[[.,[[.,[.,.]],.]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[[[.,.],.],.]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[.,[.,.]]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[[.,.],.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,.]],[.,.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],.],[.,.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,[.,.]]],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[.,[[.,.],.]],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],[.,.]],.],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [.,[[[[.,[.,.]],.],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[[[.,.],.],.],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[.,[[.,.],.]]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[[.,.],[.,.]]]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[[.,[.,.]],.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[.,[[[.,.],.],.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,.],[.,[.,.]]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,.],[[.,.],.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,[.,.]],[.,.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[[[.,.],.],[.,.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,[.,[.,.]]],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[[.,[[.,.],.]],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[[[.,.],[.,.]],.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[[[.,[.,.]],.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[.,[[[[.,.],.],.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[.,[.,[.,.]]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[.,[[.,.],.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[[.,.],[.,.]]],.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[[.,[.,.]],.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,.],[[[.,.],.],.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,.]],[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,.]],[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],.],[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],.],[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,[.,.]]],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[[.,.],.]],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],[.,.]],[.,.]],.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,[.,.]],.],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[[.,.],.],.],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,[.,[.,.]]]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[.,[.,[[.,.],.]]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[.,[[.,.],[.,.]]],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[.,[[.,[.,.]],.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[.,[[[.,.],.],.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],[.,[.,.]]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,.],[[.,.],.]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,[.,.]],[.,.]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[[.,.],.],[.,.]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [.,[[[[.,[.,[.,.]]],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[[.,[[.,.],.]],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[[[.,.],[.,.]],.],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[[[.,[.,.]],.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [.,[[[[[[.,.],.],.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[.,[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[.,[[.,.],[.,.]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[.,[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[.,[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[.,.],[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[.,.],[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[[.,.],.],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[.,[[.,.],.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[[.,.],[.,.]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[[.,[.,.]],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[.,[[[[.,.],.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,.],[.,[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,.],[[.,.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,.],[[.,[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,.],[[[.,.],.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[.,.]],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,.],.],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,.],.],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[[.,.],.]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,.],[.,.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,[.,.]],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[[.,.],.],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[.,[[.,.],.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[[.,.],[.,.]]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[[.,[.,.]],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[.,[[[.,.],.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,.],[.,[.,.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,.],[[.,.],.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,[.,.]],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[[.,.],.],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,[.,[.,.]]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[[.,[[.,.],.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[[[.,.],[.,.]],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[[[.,[.,.]],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,.],[[[[[.,.],.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[.,[[[.,.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[.,.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[[.,.],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[.,[[.,.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[[.,.],[.,.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[[.,[.,.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,.]],[[[[.,.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[.,[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[.,[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[.,[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[.,[[[.,.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[.,.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[.,.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[.,[.,.]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[[.,.],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[.,[.,[.,.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[.,[[.,.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[[.,.],[.,.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[[.,[.,.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],.],[[[[.,.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,.]]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],.]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],.]],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],.]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],.]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,.]],[.,[[.,.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,.]],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [[[.,.],[.,.]],[[.,[.,.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,.]],[[[.,.],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],.],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],.],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],.],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],.],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],.],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],.],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],.],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],.],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,.],.]]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[.,.]]],[[.,.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,.]],.]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],.],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],.],.]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[.,.]]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,.],.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,.],.]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[.,.]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[.,.]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,.]]],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],.]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],.]],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,.]],.],[[.,.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],.],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],.],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[[.,.],.],.]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[[.,.],.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],.],[.,.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,[[.,.],.]],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],[.,.]],.]],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[.,[.,.]],.],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[[.,.],.],.],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[[.,.],.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,.],[.,.]]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,[.,.]],.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[[.,.],.],.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[[.,.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[[.,.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],.]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,[.,.]]]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[[.,.],.]]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],[.,.]]],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[.,[.,.]],.]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[[.,.],.],.]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[[.,.],.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,[.,.]]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[[.,.],.]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[.,[.,.]],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[.,[[[.,.],.],.]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,.],[[.,.],.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,[[[.,.],.],[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[.,[[.,.],.]],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[[.,.],[.,.]],.]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[[.,[.,.]],.],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[.,[[[[.,.],.],.],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[.,[[.,.],.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[[.,.],[.,.]]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[[.,[.,.]],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,.],[[[.,.],.],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,.]],[[.,.],.]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],.],[.,[.,.]]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],.],[[.,.],.]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,[[.,.],.]],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],[.,.]],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,[.,.]],.],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[[.,.],.],.],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,[.,[[.,.],.]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,[[.,.],[.,.]]],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[.,[[[.,.],.],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],[.,[.,.]]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,.],[[.,.],.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,[.,.]],[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[[.,.],.],[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[.,[[[.,[.,[.,.]]],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[.,[[.,.],.]],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[[.,.],[.,.]],.],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[[.,[.,.]],.],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[.,[[[[[.,.],.],.],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[.,[[.,.],.]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[[.,.],[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [[[.,.],[.,[[.,[.,.]],.]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[.,[[[.,.],.],.]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,.],[.,[.,.]]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,.],[[.,.],.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,[.,.]],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[[.,.],.],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,[.,[.,.]]],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[[.,[[.,.],.]],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[[[.,.],[.,.]],.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [[[.,.],[[[.,[.,.]],.],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,.],[[[[.,.],.],.],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[.,[[.,.],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[[.,.],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[[.,[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,.]],[[[.,.],.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[.,[[.,.],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[[.,.],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[[.,[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],.],[[[.,.],.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,.]]],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],.]],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],.]],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,.]],[[.,.],.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],.],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],.],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[[.,.],.]]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],[.,.]]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [[[.,[[.,[.,.]],.]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[[.,.],.],.]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[[.,.],.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,[.,.]]],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[[.,.],.]],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[5,2] [[[[[.,[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[[.,.],.],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[.,[[.,.],.]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[[.,.],[.,.]]]],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[[.,[.,.]],.]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[.,[[[.,.],.],.]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[[.,.],[[.,.],.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[[.,[.,.]],[.,.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[[[.,.],.],[.,.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[[.,.],[.,.]],.]],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[.,[[[[.,.],.],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[.,[[.,.],.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[[.,.],[.,.]]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[[.,[.,.]],.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,.],[[[.,.],.],.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,.]],[[.,.],.]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],.],[[.,.],.]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,[.,.]]],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[[.,.],.]],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],[.,.]],[.,.]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,[.,.]],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[[.,.],.],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[.,[[.,.],.]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[[.,.],[.,.]]],.],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[.,.],[.,[.,.]]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,.],[[.,.],.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,[.,.]],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[[.,.],.],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[4,3] [[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[[.,.],[.,.]],.],.],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3] [[[[[[[.,.],.],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[4,3]
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
Map
chromatic difference sequence
Description
The chromatic difference sequence of a graph.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.
Map
Foata bijection
Description
The Foata bijection for compositions.
The Foata bijection $\phi$ is a bijection on the set of words whose letters are positive integers. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index St000769The major index of a composition regarded as a word. to the number of inversions St000766The number of inversions of an integer composition..