Identifier
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00047: Ordered trees —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Images
[1,0] => [[]] => ([(0,1)],2) => ([],2)
[1,0,1,0] => [[],[]] => ([(0,2),(1,2)],3) => ([(1,2)],3)
[1,1,0,0] => [[[]]] => ([(0,2),(2,1)],3) => ([],3)
[1,0,1,0,1,0] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,0] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4)
[1,1,0,0,1,0] => [[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4)
[1,1,0,1,0,0] => [[[],[]]] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4)
[1,1,1,0,0,0] => [[[[]]]] => ([(0,3),(2,1),(3,2)],4) => ([],4)
[1,0,1,0,1,0,1,0] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,1,0,0] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,1,0,0,1,0] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,1,0,1,0,0] => [[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,1,1,0,0,0] => [[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5)
[1,1,0,0,1,0,1,0] => [[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,1,0,0,1,1,0,0] => [[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,0] => [[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(1,4),(2,3),(2,4),(3,4)],5)
[1,1,0,1,0,1,0,0] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([(2,3),(2,4),(3,4)],5)
[1,1,0,1,1,0,0,0] => [[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5)
[1,1,1,0,0,0,1,0] => [[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(1,4),(2,4),(3,4)],5)
[1,1,1,0,0,1,0,0] => [[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5)
[1,1,1,0,1,0,0,0] => [[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(3,4)],5)
[1,1,1,1,0,0,0,0] => [[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5)
[1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(1,5),(2,5),(3,5),(4,5)],6)
[1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(2,5),(3,4),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(2,5),(3,4),(3,5),(4,5)],6)
[1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(3,4),(3,5),(4,5)],6)
[1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6)
[1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(1,5),(2,5),(3,5),(4,5)],6)
[1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(2,5),(3,5),(4,5)],6)
[1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6)
[1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6)
[1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6)
[1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,0] => [[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,1,0,0,0] => [[],[],[[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0] => [[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,0] => [[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,0] => [[],[[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,0] => [[],[[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
>>> Load all 308 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,0] => [[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,0] => [[[],[]],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,0] => [[[],[]],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,0] => [[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,0] => [[[],[[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,0] => [[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,0] => [[[],[[]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,0] => [[[],[[],[]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,0] => [[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,0] => [[[],[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,0] => [[[],[[[]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,0] => [[[],[[[],[]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,0] => [[[[]]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,0] => [[[[]]],[[[]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[[]],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,0] => [[[[]],[]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,0] => [[[[]],[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,0] => [[[[]],[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,0] => [[[[]],[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,0] => [[[[]],[[[]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,0,1,1,0,0] => [[[[],[]]],[[]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,0] => [[[[],[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,1,1,0,0,0] => [[[[],[]],[[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,0] => [[[[],[],[[]]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,0] => [[[[],[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,0] => [[[[],[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,0] => [[[[],[[[]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,0] => [[[[[]]]],[[]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,0] => [[[[[]]],[]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,0,1,0] => [[[[[]],[]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,0] => [[[[[],[]]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,0] => [[[[[],[]]],[]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([(3,6),(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => ([(4,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,0] => [[[[[],[[]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(4,6),(5,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(3,6),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(4,6),(5,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => ([(5,6)],7)
[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) => ([],7)
[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) => ([],8)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[],[[],[[],[]]]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[],[[],[[[],[]],[]]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[],[[[],[]],[[],[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9) => ([(1,8),(2,3),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[],[[[],[[],[]]],[]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[],[[[[],[]],[]],[]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[],[]],[[],[[],[]]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(1,5),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(6,7),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[],[]],[[[],[]],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(1,5),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(6,7),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[],[[],[]]],[[],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(1,5),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(6,7),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[],[[],[[],[]]]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[],[[[],[]],[]]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[],[]],[]],[[],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(1,5),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(6,7),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[[[],[]],[[],[]]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9) => ([(1,8),(2,3),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[],[[],[]]],[]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[],[]],[]],[]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[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) => ([],9)
[] => [] => ([],1) => ([],1)
[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) => ([],10)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[],[[],[[],[[],[]]]]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[],[[],[[[],[]],[[],[]]]]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[]],[[],[[],[]]]]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(1,10),(2,6),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[],[[[],[[],[]]],[[],[]]]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(1,10),(2,6),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[],[[[[],[]],[]],[[],[]]]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(1,10),(2,6),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[],[[[],[[],[[],[]]]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[],[[[],[[[],[]],[]]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]],[[],[]]],[]]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[],[[[[],[[],[]]],[]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[],[[[[[],[]],[]],[]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[],[]],[[],[[],[[],[]]]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[],[]],[[[],[]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => ([(1,8),(1,9),(1,10),(2,3),(2,6),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(9,10)],11)
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[],[]],[[[],[[],[]]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[],[]],[[[[],[]],[]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]],[[],[[],[]]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(1,2),(1,4),(1,7),(1,8),(1,10),(2,3),(2,5),(2,6),(2,9),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[],[[],[]]],[[[],[]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(1,2),(1,4),(1,7),(1,8),(1,10),(2,3),(2,5),(2,6),(2,9),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[[],[]],[]],[[],[[],[]]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(1,2),(1,4),(1,7),(1,8),(1,10),(2,3),(2,5),(2,6),(2,9),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]],[[[],[]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(1,2),(1,4),(1,7),(1,8),(1,10),(2,3),(2,5),(2,6),(2,9),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[],[[],[[],[]]]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[],[[[],[]],[]]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[],[]],[[],[]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => ([(1,8),(1,9),(1,10),(2,3),(2,6),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(9,10)],11)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[],[[],[]]],[]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[[],[]],[]],[]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[[],[]],[]],[]],[]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(1,10),(2,9),(2,10),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[],[[],[[],[[],[[],[[],[]]]]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [[],[[],[[],[[[],[]],[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[],[[[],[]],[[],[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [[],[[],[[[],[[],[]]],[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[],[[],[[[[],[]],[]],[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[[],[]],[[],[[],[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,11),(9,12),(11,9),(12,10)],13) => ([(1,12),(2,8),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[],[[[],[]],[[[],[]],[[],[]]]]] => ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(11,12),(12,10)],13) => ([(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]],[[],[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,11),(5,10),(6,9),(7,10),(8,11),(10,12),(11,12),(12,9)],13) => ([(1,12),(2,3),(2,5),(2,8),(2,9),(2,11),(2,12),(3,4),(3,6),(3,7),(3,10),(3,12),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[[],[]],[]],[[],[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,11),(5,10),(6,9),(7,10),(8,11),(10,12),(11,12),(12,9)],13) => ([(1,12),(2,3),(2,5),(2,8),(2,9),(2,11),(2,12),(3,4),(3,6),(3,7),(3,10),(3,12),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [[],[[[],[[],[[],[]]]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,11),(9,12),(11,9),(12,10)],13) => ([(1,12),(2,8),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [[],[[[],[[[],[]],[]]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,11),(9,12),(11,9),(12,10)],13) => ([(1,12),(2,8),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[],[[[[],[]],[[],[]]],[[],[]]]] => ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(11,12),(12,10)],13) => ([(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [[],[[[[],[[],[]]],[]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,11),(9,12),(11,9),(12,10)],13) => ([(1,12),(2,8),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[],[[[[[],[]],[]],[]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,11),(9,12),(11,9),(12,10)],13) => ([(1,12),(2,8),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[],[[[],[[],[[],[[],[]]]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [[],[[[],[[],[[[],[]],[]]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[],[[[],[[[],[]],[[],[]]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [[],[[[],[[[],[[],[]]],[]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[],[[[],[[[[],[]],[]],[]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[],[[[[],[]],[[],[[],[]]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[],[[[[],[]],[[[],[]],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[[],[]]],[[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[],[[[[[],[]],[]],[[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [[],[[[[],[[],[[],[]]]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[],[[[[],[[[],[]],[]]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[],[[[[[],[]],[[],[]]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[],[[[[[],[[],[]]],[]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[],[[[[[[],[]],[]],[]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[],[]],[[],[[],[[],[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[[],[]],[[],[[[],[]],[[],[]]]]] => ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(10,12),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[],[]],[[[],[]],[[],[[],[]]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[[],[]],[[[],[[],[]]],[[],[]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[[],[]],[[[[],[]],[]],[[],[]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[],[]],[[[],[[],[[],[]]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[],[]],[[[],[[[],[]],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[],[]],[[[[],[]],[[],[]]],[]]] => ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(10,12),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[[],[]],[[[[],[[],[]]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[],[]],[[[[[],[]],[]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[],[[],[]]],[[],[[],[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[],[[],[]]],[[[],[]],[[],[]]]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,9),(6,9),(7,11),(8,11),(9,10),(10,12),(11,12)],13) => ([(1,2),(1,5),(1,10),(1,11),(1,12),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[],[[],[]]],[[[],[[],[]]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[],[[],[]]],[[[[],[]],[]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[]],[]],[[],[[],[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[[],[]],[]],[[[],[]],[[],[]]]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,9),(6,9),(7,11),(8,11),(9,10),(10,12),(11,12)],13) => ([(1,2),(1,5),(1,10),(1,11),(1,12),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[[],[]],[]],[[[],[[],[]]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[],[]],[]],[[[[],[]],[]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[],[[],[[],[]]]],[[],[[],[]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[],[[],[[],[]]]],[[[],[]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[],[[[],[]],[]]],[[],[[],[]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[],[[[],[]],[]]],[[[],[]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[[],[]],[[],[]]],[[],[[],[]]]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,9),(6,9),(7,11),(8,11),(9,10),(10,12),(11,12)],13) => ([(1,2),(1,5),(1,10),(1,11),(1,12),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[[],[]]],[[[],[]],[]]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,9),(6,9),(7,11),(8,11),(9,10),(10,12),(11,12)],13) => ([(1,2),(1,5),(1,10),(1,11),(1,12),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[[],[[],[]]],[]],[[],[[],[]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[[],[[],[]]],[]],[[[],[]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[[[],[]],[]],[]],[[],[[],[]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[[[],[]],[]],[]],[[[],[]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[[],[[],[[],[[],[]]]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[[],[[],[[[],[]],[]]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[],[[[],[]],[[],[]]]],[[],[]]] => ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(10,12),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[[],[[[],[[],[]]],[]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[],[[[[],[]],[]],[]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[[],[]],[[],[[],[]]]],[[],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[[],[]],[[[],[]],[]]],[[],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[],[[],[]]],[[],[]]],[[],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[[],[]],[]],[[],[]]],[[],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[],[[],[[],[]]]],[]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[],[[[],[]],[]]],[]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[[],[]],[[],[]]],[]],[[],[]]] => ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(10,12),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[[],[[],[]]],[]],[]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[[[],[]],[]],[]],[]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
incomparability graph
Description
The incomparability graph of a poset.