Identifier
Values
[1] => [1,0,1,0] => [.,[.,.]] => ([(0,1)],2) => 1
[2] => [1,1,0,0,1,0] => [[.,.],[.,.]] => ([(0,2),(1,2)],3) => 2
[1,1] => [1,0,1,1,0,0] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 1
[3] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 2
[2,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,1] => [1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 2
[2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,2] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4) => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 1
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(4,2)],5) => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
>>> Load all 553 entries. <<<
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9) => 2
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[.,.]],[.,.]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10) => 2
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 4
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[2,2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[7,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9) => 2
[8,7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[7,6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[8,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[5,4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[7,6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[6,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[6,5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[6,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
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Description
The number of maximal chains in a poset.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.