Processing math: 5%

Your data matches 30 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001605
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,3,1]
 => [3,1]
 => [2,1,1]
 => 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,3]
 => [3]
 => [1,1,1]
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,1]
 => [3,1]
 => [2,1,1]
 => 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,3]
 => [3]
 => [1,1,1]
 => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [3,3,1]
 => [3,1]
 => [2,1,1]
 => 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,3]
 => [3]
 => [1,1,1]
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,3]
 => [3]
 => [1,1,1]
 => 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [5]
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [5]
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [5]
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [5]
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [3]
 => 1
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition. Two colourings are considered equal, if they are obtained by an action of the cyclic group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001651
(load all 4 compositions to match this statistic)
Mapping
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001651: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,27),(8,28),(8,30),(8,45),(9,27),(9,29),(9,31),(9,46),(10,28),(10,29),(10,32),(10,47),(11,30),(11,31),(11,32),(11,48),(12,33),(12,34),(12,36),(12,45),(13,33),(13,35),(13,37),(13,46),(14,34),(14,35),(14,38),(14,47),(15,36),(15,37),(15,38),(15,48),(16,39),(16,40),(16,42),(16,45),(17,39),(17,41),(17,43),(17,46),(18,40),(18,41),(18,44),(18,47),(19,42),(19,43),(19,44),(19,48),(20,27),(20,33),(20,39),(20,55),(21,28),(21,34),(21,40),(21,55),(22,29),(22,35),(22,41),(22,55),(23,30),(23,36),(23,42),(23,55),(24,31),(24,37),(24,43),(24,55),(25,32),(25,38),(25,44),(25,55),(26,45),(26,46),(26,47),(26,48),(27,51),(27,56),(28,49),(28,56),(29,50),(29,56),(30,52),(30,56),(31,53),(31,56),(32,54),(32,56),(33,51),(33,57),(34,49),(34,57),(35,50),(35,57),(36,52),(36,57),(37,53),(37,57),(38,54),(38,57),(39,51),(39,58),(40,49),(40,58),(41,50),(41,58),(42,52),(42,58),(43,53),(43,58),(44,54),(44,58),(45,49),(45,51),(45,52),(46,50),(46,51),(46,53),(47,49),(47,50),(47,54),(48,52),(48,53),(48,54),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,56),(55,57),(55,58),(56,59),(57,59),(58,59)],60)
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,17),(1,23),(1,30),(1,42),(1,44),(2,10),(2,16),(2,22),(2,30),(2,41),(2,43),(3,12),(3,18),(3,24),(3,29),(3,41),(3,44),(4,13),(4,19),(4,25),(4,29),(4,42),(4,43),(5,15),(5,21),(5,27),(5,28),(5,43),(5,44),(6,14),(6,20),(6,26),(6,28),(6,41),(6,42),(7,22),(7,23),(7,24),(7,25),(7,26),(7,27),(7,31),(8,16),(8,17),(8,18),(8,19),(8,20),(8,21),(8,31),(9,10),(9,11),(9,12),(9,13),(9,14),(9,15),(9,31),(10,32),(10,45),(10,47),(10,57),(11,32),(11,46),(11,48),(11,58),(12,33),(12,45),(12,48),(12,59),(13,33),(13,46),(13,47),(13,60),(14,34),(14,45),(14,46),(14,61),(15,34),(15,47),(15,48),(15,62),(16,35),(16,49),(16,51),(16,57),(17,35),(17,50),(17,52),(17,58),(18,36),(18,49),(18,52),(18,59),(19,36),(19,50),(19,51),(19,60),(20,37),(20,49),(20,50),(20,61),(21,37),(21,51),(21,52),(21,62),(22,38),(22,53),(22,55),(22,57),(23,38),(23,54),(23,56),(23,58),(24,39),(24,53),(24,56),(24,59),(25,39),(25,54),(25,55),(25,60),(26,40),(26,53),(26,54),(26,61),(27,40),(27,55),(27,56),(27,62),(28,34),(28,37),(28,40),(28,70),(29,33),(29,36),(29,39),(29,70),(30,32),(30,35),(30,38),(30,70),(31,57),(31,58),(31,59),(31,60),(31,61),(31,62),(32,63),(32,71),(33,64),(33,71),(34,65),(34,71),(35,63),(35,72),(36,64),(36,72),(37,65),(37,72),(38,63),(38,73),(39,64),(39,73),(40,65),(40,73),(41,45),(41,49),(41,53),(41,70),(42,46),(42,50),(42,54),(42,70),(43,47),(43,51),(43,55),(43,70),(44,48),(44,52),(44,56),(44,70),(45,66),(45,71),(46,67),(46,71),(47,68),(47,71),(48,69),(48,71),(49,66),(49,72),(50,67),(50,72),(51,68),(51,72),(52,69),(52,72),(53,66),(53,73),(54,67),(54,73),(55,68),(55,73),(56,69),(56,73),(57,63),(57,66),(57,68),(58,63),(58,67),(58,69),(59,64),(59,66),(59,69),(60,64),(60,67),(60,68),(61,65),(61,66),(61,67),(62,65),(62,68),(62,69),(63,74),(64,74),(65,74),(66,74),(67,74),(68,74),(69,74),(70,71),(70,72),(70,73),(71,74),(72,74),(73,74)],75)
 => ? = 2 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ? = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,24),(1,25),(1,26),(1,27),(1,28),(1,29),(1,30),(2,18),(2,19),(2,20),(2,21),(2,22),(2,23),(2,30),(3,15),(3,16),(3,17),(3,20),(3,26),(3,56),(4,12),(4,13),(4,14),(4,19),(4,25),(4,56),(5,9),(5,10),(5,11),(5,18),(5,24),(5,56),(6,11),(6,14),(6,17),(6,23),(6,29),(6,55),(7,10),(7,13),(7,16),(7,22),(7,28),(7,55),(8,9),(8,12),(8,15),(8,21),(8,27),(8,55),(9,31),(9,40),(9,66),(9,69),(10,32),(10,41),(10,67),(10,69),(11,33),(11,42),(11,68),(11,69),(12,34),(12,43),(12,66),(12,70),(13,35),(13,44),(13,67),(13,70),(14,36),(14,45),(14,68),(14,70),(15,37),(15,46),(15,66),(15,71),(16,38),(16,47),(16,67),(16,71),(17,39),(17,48),(17,68),(17,71),(18,31),(18,32),(18,33),(18,49),(18,72),(19,34),(19,35),(19,36),(19,50),(19,72),(20,37),(20,38),(20,39),(20,51),(20,72),(21,31),(21,34),(21,37),(21,52),(21,73),(22,32),(22,35),(22,38),(22,53),(22,73),(23,33),(23,36),(23,39),(23,54),(23,73),(24,40),(24,41),(24,42),(24,49),(24,74),(25,43),(25,44),(25,45),(25,50),(25,74),(26,46),(26,47),(26,48),(26,51),(26,74),(27,40),(27,43),(27,46),(27,52),(27,75),(28,41),(28,44),(28,47),(28,53),(28,75),(29,42),(29,45),(29,48),(29,54),(29,75),(30,49),(30,50),(30,51),(30,52),(30,53),(30,54),(31,57),(31,78),(31,81),(32,58),(32,79),(32,81),(33,59),(33,80),(33,81),(34,60),(34,78),(34,82),(35,61),(35,79),(35,82),(36,62),(36,80),(36,82),(37,63),(37,78),(37,83),(38,64),(38,79),(38,83),(39,65),(39,80),(39,83),(40,57),(40,84),(40,87),(41,58),(41,85),(41,87),(42,59),(42,86),(42,87),(43,60),(43,84),(43,88),(44,61),(44,85),(44,88),(45,62),(45,86),(45,88),(46,63),(46,84),(46,89),(47,64),(47,85),(47,89),(48,65),(48,86),(48,89),(49,57),(49,58),(49,59),(49,76),(50,60),(50,61),(50,62),(50,76),(51,63),(51,64),(51,65),(51,76),(52,57),(52,60),(52,63),(52,77),(53,58),(53,61),(53,64),(53,77),(54,59),(54,62),(54,65),(54,77),(55,69),(55,70),(55,71),(55,73),(55,75),(56,66),(56,67),(56,68),(56,72),(56,74),(57,90),(57,93),(58,91),(58,93),(59,92),(59,93),(60,90),(60,94),(61,91),(61,94),(62,92),(62,94),(63,90),(63,95),(64,91),(64,95),(65,92),(65,95),(66,78),(66,84),(66,96),(67,79),(67,85),(67,96),(68,80),(68,86),(68,96),(69,81),(69,87),(69,96),(70,82),(70,88),(70,96),(71,83),(71,89),(71,96),(72,76),(72,78),(72,79),(72,80),(73,77),(73,81),(73,82),(73,83),(74,76),(74,84),(74,85),(74,86),(75,77),(75,87),(75,88),(75,89),(76,90),(76,91),(76,92),(77,93),(77,94),(77,95),(78,90),(78,97),(79,91),(79,97),(80,92),(80,97),(81,93),(81,97),(82,94),(82,97),(83,95),(83,97),(84,90),(84,98),(85,91),(85,98),(86,92),(86,98),(87,93),(87,98),(88,94),(88,98),(89,95),(89,98),(90,99),(91,99),(92,99),(93,99),(94,99),(95,99),(96,97),(96,98),(97,99),(98,99)],100)
 => ? = 4 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ? = 1 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1 - 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,27),(8,28),(8,30),(8,45),(9,27),(9,29),(9,31),(9,46),(10,28),(10,29),(10,32),(10,47),(11,30),(11,31),(11,32),(11,48),(12,33),(12,34),(12,36),(12,45),(13,33),(13,35),(13,37),(13,46),(14,34),(14,35),(14,38),(14,47),(15,36),(15,37),(15,38),(15,48),(16,39),(16,40),(16,42),(16,45),(17,39),(17,41),(17,43),(17,46),(18,40),(18,41),(18,44),(18,47),(19,42),(19,43),(19,44),(19,48),(20,27),(20,33),(20,39),(20,55),(21,28),(21,34),(21,40),(21,55),(22,29),(22,35),(22,41),(22,55),(23,30),(23,36),(23,42),(23,55),(24,31),(24,37),(24,43),(24,55),(25,32),(25,38),(25,44),(25,55),(26,45),(26,46),(26,47),(26,48),(27,51),(27,56),(28,49),(28,56),(29,50),(29,56),(30,52),(30,56),(31,53),(31,56),(32,54),(32,56),(33,51),(33,57),(34,49),(34,57),(35,50),(35,57),(36,52),(36,57),(37,53),(37,57),(38,54),(38,57),(39,51),(39,58),(40,49),(40,58),(41,50),(41,58),(42,52),(42,58),(43,53),(43,58),(44,54),(44,58),(45,49),(45,51),(45,52),(46,50),(46,51),(46,53),(47,49),(47,50),(47,54),(48,52),(48,53),(48,54),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,56),(55,57),(55,58),(56,59),(57,59),(58,59)],60)
 => ? = 2 - 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3 - 1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ? = 1 - 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,16),(1,20),(1,27),(1,28),(1,29),(1,33),(2,11),(2,15),(2,19),(2,25),(2,26),(2,29),(2,32),(3,10),(3,14),(3,18),(3,24),(3,26),(3,28),(3,31),(4,9),(4,13),(4,17),(4,24),(4,25),(4,27),(4,30),(5,21),(5,22),(5,23),(5,30),(5,31),(5,32),(5,33),(6,17),(6,18),(6,19),(6,20),(6,23),(6,34),(7,13),(7,14),(7,15),(7,16),(7,22),(7,34),(8,9),(8,10),(8,11),(8,12),(8,21),(8,34),(9,41),(9,42),(9,44),(9,59),(9,89),(10,41),(10,43),(10,45),(10,60),(10,90),(11,42),(11,43),(11,46),(11,61),(11,91),(12,44),(12,45),(12,46),(12,62),(12,92),(13,47),(13,48),(13,50),(13,63),(13,89),(14,47),(14,49),(14,51),(14,64),(14,90),(15,48),(15,49),(15,52),(15,65),(15,91),(16,50),(16,51),(16,52),(16,66),(16,92),(17,53),(17,54),(17,56),(17,67),(17,89),(18,53),(18,55),(18,57),(18,68),(18,90),(19,54),(19,55),(19,58),(19,69),(19,91),(20,56),(20,57),(20,58),(20,70),(20,92),(21,59),(21,60),(21,61),(21,62),(21,93),(22,63),(22,64),(22,65),(22,66),(22,93),(23,67),(23,68),(23,69),(23,70),(23,93),(24,37),(24,41),(24,47),(24,53),(24,104),(25,35),(25,42),(25,48),(25,54),(25,104),(26,36),(26,43),(26,49),(26,55),(26,104),(27,38),(27,44),(27,50),(27,56),(27,104),(28,39),(28,45),(28,51),(28,57),(28,104),(29,40),(29,46),(29,52),(29,58),(29,104),(30,35),(30,37),(30,38),(30,59),(30,63),(30,67),(31,36),(31,37),(31,39),(31,60),(31,64),(31,68),(32,35),(32,36),(32,40),(32,61),(32,65),(32,69),(33,38),(33,39),(33,40),(33,62),(33,66),(33,70),(34,89),(34,90),(34,91),(34,92),(34,93),(35,71),(35,77),(35,83),(35,114),(36,72),(36,78),(36,84),(36,114),(37,73),(37,79),(37,85),(37,114),(38,74),(38,80),(38,86),(38,114),(39,75),(39,81),(39,87),(39,114),(40,76),(40,82),(40,88),(40,114),(41,73),(41,96),(41,111),(42,71),(42,94),(42,111),(43,72),(43,95),(43,111),(44,74),(44,97),(44,111),(45,75),(45,98),(45,111),(46,76),(46,99),(46,111),(47,79),(47,96),(47,112),(48,77),(48,94),(48,112),(49,78),(49,95),(49,112),(50,80),(50,97),(50,112),(51,81),(51,98),(51,112),(52,82),(52,99),(52,112),(53,85),(53,96),(53,113),(54,83),(54,94),(54,113),(55,84),(55,95),(55,113),(56,86),(56,97),(56,113),(57,87),(57,98),(57,113),(58,88),(58,99),(58,113),(59,71),(59,73),(59,74),(59,100),(60,72),(60,73),(60,75),(60,101),(61,71),(61,72),(61,76),(61,102),(62,74),(62,75),(62,76),(62,103),(63,77),(63,79),(63,80),(63,100),(64,78),(64,79),(64,81),(64,101),(65,77),(65,78),(65,82),(65,102),(66,80),(66,81),(66,82),(66,103),(67,83),(67,85),(67,86),(67,100),(68,84),(68,85),(68,87),(68,101),(69,83),(69,84),(69,88),(69,102),(70,86),(70,87),(70,88),(70,103),(71,105),(71,115),(72,106),(72,115),(73,107),(73,115),(74,108),(74,115),(75,109),(75,115),(76,110),(76,115),(77,105),(77,116),(78,106),(78,116),(79,107),(79,116),(80,108),(80,116),(81,109),(81,116),(82,110),(82,116),(83,105),(83,117),(84,106),(84,117),(85,107),(85,117),(86,108),(86,117),(87,109),(87,117),(88,110),(88,117),(89,94),(89,96),(89,97),(89,100),(90,95),(90,96),(90,98),(90,101),(91,94),(91,95),(91,99),(91,102),(92,97),(92,98),(92,99),(92,103),(93,100),(93,101),(93,102),(93,103),(94,105),(94,118),(95,106),(95,118),(96,107),(96,118),(97,108),(97,118),(98,109),(98,118),(99,110),(99,118),(100,105),(100,107),(100,108),(101,106),(101,107),(101,109),(102,105),(102,106),(102,110),(103,108),(103,109),(103,110),(104,111),(104,112),(104,113),(104,114),(105,119),(106,119),(107,119),(108,119),(109,119),(110,119),(111,115),(111,118),(112,116),(112,118),(113,117),(113,118),(114,115),(114,116),(114,117),(115,119),(116,119),(117,119),(118,119)],120)
 => ? = 3 - 1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ? = 1 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 0 = 1 - 1
Description
The Frankl number of a lattice. For a lattice L on at least two elements, this is max where we maximize over all join irreducible elements and [x, 1] denotes the interval from x to the top element. Frankl's conjecture asserts that this number is non-negative, and zero if and only if L is a Boolean lattice.
Matching statistic: St000068
(load all 2 compositions to match this statistic)
Mapping
Mp00266: Graphs —connected vertex partitions⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000068: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,27),(8,28),(8,30),(8,45),(9,27),(9,29),(9,31),(9,46),(10,28),(10,29),(10,32),(10,47),(11,30),(11,31),(11,32),(11,48),(12,33),(12,34),(12,36),(12,45),(13,33),(13,35),(13,37),(13,46),(14,34),(14,35),(14,38),(14,47),(15,36),(15,37),(15,38),(15,48),(16,39),(16,40),(16,42),(16,45),(17,39),(17,41),(17,43),(17,46),(18,40),(18,41),(18,44),(18,47),(19,42),(19,43),(19,44),(19,48),(20,27),(20,33),(20,39),(20,55),(21,28),(21,34),(21,40),(21,55),(22,29),(22,35),(22,41),(22,55),(23,30),(23,36),(23,42),(23,55),(24,31),(24,37),(24,43),(24,55),(25,32),(25,38),(25,44),(25,55),(26,45),(26,46),(26,47),(26,48),(27,51),(27,56),(28,49),(28,56),(29,50),(29,56),(30,52),(30,56),(31,53),(31,56),(32,54),(32,56),(33,51),(33,57),(34,49),(34,57),(35,50),(35,57),(36,52),(36,57),(37,53),(37,57),(38,54),(38,57),(39,51),(39,58),(40,49),(40,58),(41,50),(41,58),(42,52),(42,58),(43,53),(43,58),(44,54),(44,58),(45,49),(45,51),(45,52),(46,50),(46,51),(46,53),(47,49),(47,50),(47,54),(48,52),(48,53),(48,54),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,56),(55,57),(55,58),(56,59),(57,59),(58,59)],60)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,27),(8,28),(8,30),(8,45),(9,27),(9,29),(9,31),(9,46),(10,28),(10,29),(10,32),(10,47),(11,30),(11,31),(11,32),(11,48),(12,33),(12,34),(12,36),(12,45),(13,33),(13,35),(13,37),(13,46),(14,34),(14,35),(14,38),(14,47),(15,36),(15,37),(15,38),(15,48),(16,39),(16,40),(16,42),(16,45),(17,39),(17,41),(17,43),(17,46),(18,40),(18,41),(18,44),(18,47),(19,42),(19,43),(19,44),(19,48),(20,27),(20,33),(20,39),(20,55),(21,28),(21,34),(21,40),(21,55),(22,29),(22,35),(22,41),(22,55),(23,30),(23,36),(23,42),(23,55),(24,31),(24,37),(24,43),(24,55),(25,32),(25,38),(25,44),(25,55),(26,45),(26,46),(26,47),(26,48),(27,51),(27,56),(28,49),(28,56),(29,50),(29,56),(30,52),(30,56),(31,53),(31,56),(32,54),(32,56),(33,51),(33,57),(34,49),(34,57),(35,50),(35,57),(36,52),(36,57),(37,53),(37,57),(38,54),(38,57),(39,51),(39,58),(40,49),(40,58),(41,50),(41,58),(42,52),(42,58),(43,53),(43,58),(44,54),(44,58),(45,49),(45,51),(45,52),(46,50),(46,51),(46,53),(47,49),(47,50),(47,54),(48,52),(48,53),(48,54),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,56),(55,57),(55,58),(56,59),(57,59),(58,59)],60)
 => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,17),(1,23),(1,30),(1,42),(1,44),(2,10),(2,16),(2,22),(2,30),(2,41),(2,43),(3,12),(3,18),(3,24),(3,29),(3,41),(3,44),(4,13),(4,19),(4,25),(4,29),(4,42),(4,43),(5,15),(5,21),(5,27),(5,28),(5,43),(5,44),(6,14),(6,20),(6,26),(6,28),(6,41),(6,42),(7,22),(7,23),(7,24),(7,25),(7,26),(7,27),(7,31),(8,16),(8,17),(8,18),(8,19),(8,20),(8,21),(8,31),(9,10),(9,11),(9,12),(9,13),(9,14),(9,15),(9,31),(10,32),(10,45),(10,47),(10,57),(11,32),(11,46),(11,48),(11,58),(12,33),(12,45),(12,48),(12,59),(13,33),(13,46),(13,47),(13,60),(14,34),(14,45),(14,46),(14,61),(15,34),(15,47),(15,48),(15,62),(16,35),(16,49),(16,51),(16,57),(17,35),(17,50),(17,52),(17,58),(18,36),(18,49),(18,52),(18,59),(19,36),(19,50),(19,51),(19,60),(20,37),(20,49),(20,50),(20,61),(21,37),(21,51),(21,52),(21,62),(22,38),(22,53),(22,55),(22,57),(23,38),(23,54),(23,56),(23,58),(24,39),(24,53),(24,56),(24,59),(25,39),(25,54),(25,55),(25,60),(26,40),(26,53),(26,54),(26,61),(27,40),(27,55),(27,56),(27,62),(28,34),(28,37),(28,40),(28,70),(29,33),(29,36),(29,39),(29,70),(30,32),(30,35),(30,38),(30,70),(31,57),(31,58),(31,59),(31,60),(31,61),(31,62),(32,63),(32,71),(33,64),(33,71),(34,65),(34,71),(35,63),(35,72),(36,64),(36,72),(37,65),(37,72),(38,63),(38,73),(39,64),(39,73),(40,65),(40,73),(41,45),(41,49),(41,53),(41,70),(42,46),(42,50),(42,54),(42,70),(43,47),(43,51),(43,55),(43,70),(44,48),(44,52),(44,56),(44,70),(45,66),(45,71),(46,67),(46,71),(47,68),(47,71),(48,69),(48,71),(49,66),(49,72),(50,67),(50,72),(51,68),(51,72),(52,69),(52,72),(53,66),(53,73),(54,67),(54,73),(55,68),(55,73),(56,69),(56,73),(57,63),(57,66),(57,68),(58,63),(58,67),(58,69),(59,64),(59,66),(59,69),(60,64),(60,67),(60,68),(61,65),(61,66),(61,67),(62,65),(62,68),(62,69),(63,74),(64,74),(65,74),(66,74),(67,74),(68,74),(69,74),(70,71),(70,72),(70,73),(71,74),(72,74),(73,74)],75)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,17),(1,23),(1,30),(1,42),(1,44),(2,10),(2,16),(2,22),(2,30),(2,41),(2,43),(3,12),(3,18),(3,24),(3,29),(3,41),(3,44),(4,13),(4,19),(4,25),(4,29),(4,42),(4,43),(5,15),(5,21),(5,27),(5,28),(5,43),(5,44),(6,14),(6,20),(6,26),(6,28),(6,41),(6,42),(7,22),(7,23),(7,24),(7,25),(7,26),(7,27),(7,31),(8,16),(8,17),(8,18),(8,19),(8,20),(8,21),(8,31),(9,10),(9,11),(9,12),(9,13),(9,14),(9,15),(9,31),(10,32),(10,45),(10,47),(10,57),(11,32),(11,46),(11,48),(11,58),(12,33),(12,45),(12,48),(12,59),(13,33),(13,46),(13,47),(13,60),(14,34),(14,45),(14,46),(14,61),(15,34),(15,47),(15,48),(15,62),(16,35),(16,49),(16,51),(16,57),(17,35),(17,50),(17,52),(17,58),(18,36),(18,49),(18,52),(18,59),(19,36),(19,50),(19,51),(19,60),(20,37),(20,49),(20,50),(20,61),(21,37),(21,51),(21,52),(21,62),(22,38),(22,53),(22,55),(22,57),(23,38),(23,54),(23,56),(23,58),(24,39),(24,53),(24,56),(24,59),(25,39),(25,54),(25,55),(25,60),(26,40),(26,53),(26,54),(26,61),(27,40),(27,55),(27,56),(27,62),(28,34),(28,37),(28,40),(28,70),(29,33),(29,36),(29,39),(29,70),(30,32),(30,35),(30,38),(30,70),(31,57),(31,58),(31,59),(31,60),(31,61),(31,62),(32,63),(32,71),(33,64),(33,71),(34,65),(34,71),(35,63),(35,72),(36,64),(36,72),(37,65),(37,72),(38,63),(38,73),(39,64),(39,73),(40,65),(40,73),(41,45),(41,49),(41,53),(41,70),(42,46),(42,50),(42,54),(42,70),(43,47),(43,51),(43,55),(43,70),(44,48),(44,52),(44,56),(44,70),(45,66),(45,71),(46,67),(46,71),(47,68),(47,71),(48,69),(48,71),(49,66),(49,72),(50,67),(50,72),(51,68),(51,72),(52,69),(52,72),(53,66),(53,73),(54,67),(54,73),(55,68),(55,73),(56,69),(56,73),(57,63),(57,66),(57,68),(58,63),(58,67),(58,69),(59,64),(59,66),(59,69),(60,64),(60,67),(60,68),(61,65),(61,66),(61,67),(62,65),(62,68),(62,69),(63,74),(64,74),(65,74),(66,74),(67,74),(68,74),(69,74),(70,71),(70,72),(70,73),(71,74),(72,74),(73,74)],75)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ?
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ?
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ?
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ?
 => ? = 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,24),(1,25),(1,26),(1,27),(1,28),(1,29),(1,30),(2,18),(2,19),(2,20),(2,21),(2,22),(2,23),(2,30),(3,15),(3,16),(3,17),(3,20),(3,26),(3,56),(4,12),(4,13),(4,14),(4,19),(4,25),(4,56),(5,9),(5,10),(5,11),(5,18),(5,24),(5,56),(6,11),(6,14),(6,17),(6,23),(6,29),(6,55),(7,10),(7,13),(7,16),(7,22),(7,28),(7,55),(8,9),(8,12),(8,15),(8,21),(8,27),(8,55),(9,31),(9,40),(9,66),(9,69),(10,32),(10,41),(10,67),(10,69),(11,33),(11,42),(11,68),(11,69),(12,34),(12,43),(12,66),(12,70),(13,35),(13,44),(13,67),(13,70),(14,36),(14,45),(14,68),(14,70),(15,37),(15,46),(15,66),(15,71),(16,38),(16,47),(16,67),(16,71),(17,39),(17,48),(17,68),(17,71),(18,31),(18,32),(18,33),(18,49),(18,72),(19,34),(19,35),(19,36),(19,50),(19,72),(20,37),(20,38),(20,39),(20,51),(20,72),(21,31),(21,34),(21,37),(21,52),(21,73),(22,32),(22,35),(22,38),(22,53),(22,73),(23,33),(23,36),(23,39),(23,54),(23,73),(24,40),(24,41),(24,42),(24,49),(24,74),(25,43),(25,44),(25,45),(25,50),(25,74),(26,46),(26,47),(26,48),(26,51),(26,74),(27,40),(27,43),(27,46),(27,52),(27,75),(28,41),(28,44),(28,47),(28,53),(28,75),(29,42),(29,45),(29,48),(29,54),(29,75),(30,49),(30,50),(30,51),(30,52),(30,53),(30,54),(31,57),(31,78),(31,81),(32,58),(32,79),(32,81),(33,59),(33,80),(33,81),(34,60),(34,78),(34,82),(35,61),(35,79),(35,82),(36,62),(36,80),(36,82),(37,63),(37,78),(37,83),(38,64),(38,79),(38,83),(39,65),(39,80),(39,83),(40,57),(40,84),(40,87),(41,58),(41,85),(41,87),(42,59),(42,86),(42,87),(43,60),(43,84),(43,88),(44,61),(44,85),(44,88),(45,62),(45,86),(45,88),(46,63),(46,84),(46,89),(47,64),(47,85),(47,89),(48,65),(48,86),(48,89),(49,57),(49,58),(49,59),(49,76),(50,60),(50,61),(50,62),(50,76),(51,63),(51,64),(51,65),(51,76),(52,57),(52,60),(52,63),(52,77),(53,58),(53,61),(53,64),(53,77),(54,59),(54,62),(54,65),(54,77),(55,69),(55,70),(55,71),(55,73),(55,75),(56,66),(56,67),(56,68),(56,72),(56,74),(57,90),(57,93),(58,91),(58,93),(59,92),(59,93),(60,90),(60,94),(61,91),(61,94),(62,92),(62,94),(63,90),(63,95),(64,91),(64,95),(65,92),(65,95),(66,78),(66,84),(66,96),(67,79),(67,85),(67,96),(68,80),(68,86),(68,96),(69,81),(69,87),(69,96),(70,82),(70,88),(70,96),(71,83),(71,89),(71,96),(72,76),(72,78),(72,79),(72,80),(73,77),(73,81),(73,82),(73,83),(74,76),(74,84),(74,85),(74,86),(75,77),(75,87),(75,88),(75,89),(76,90),(76,91),(76,92),(77,93),(77,94),(77,95),(78,90),(78,97),(79,91),(79,97),(80,92),(80,97),(81,93),(81,97),(82,94),(82,97),(83,95),(83,97),(84,90),(84,98),(85,91),(85,98),(86,92),(86,98),(87,93),(87,98),(88,94),(88,98),(89,95),(89,98),(90,99),(91,99),(92,99),(93,99),(94,99),(95,99),(96,97),(96,98),(97,99),(98,99)],100)
 => ?
 => ? = 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ?
 => ? = 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ?
 => ? = 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
 => ? = 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,12),(1,13),(1,17),(1,21),(1,25),(2,9),(2,10),(2,13),(2,16),(2,20),(2,24),(3,8),(3,10),(3,12),(3,15),(3,19),(3,23),(4,8),(4,9),(4,11),(4,14),(4,18),(4,22),(5,22),(5,23),(5,24),(5,25),(5,27),(5,28),(6,18),(6,19),(6,20),(6,21),(6,26),(6,28),(7,14),(7,15),(7,16),(7,17),(7,26),(7,27),(8,31),(8,37),(8,43),(8,88),(9,29),(9,35),(9,41),(9,88),(10,30),(10,36),(10,42),(10,88),(11,32),(11,38),(11,44),(11,88),(12,33),(12,39),(12,45),(12,88),(13,34),(13,40),(13,46),(13,88),(14,29),(14,31),(14,32),(14,47),(14,51),(15,30),(15,31),(15,33),(15,48),(15,52),(16,29),(16,30),(16,34),(16,49),(16,53),(17,32),(17,33),(17,34),(17,50),(17,54),(18,35),(18,37),(18,38),(18,47),(18,55),(19,36),(19,37),(19,39),(19,48),(19,56),(20,35),(20,36),(20,40),(20,49),(20,57),(21,38),(21,39),(21,40),(21,50),(21,58),(22,41),(22,43),(22,44),(22,51),(22,55),(23,42),(23,43),(23,45),(23,52),(23,56),(24,41),(24,42),(24,46),(24,53),(24,57),(25,44),(25,45),(25,46),(25,54),(25,58),(26,47),(26,48),(26,49),(26,50),(26,59),(27,51),(27,52),(27,53),(27,54),(27,59),(28,55),(28,56),(28,57),(28,58),(28,59),(29,60),(29,66),(29,89),(30,61),(30,67),(30,89),(31,62),(31,68),(31,89),(32,63),(32,69),(32,89),(33,64),(33,70),(33,89),(34,65),(34,71),(34,89),(35,60),(35,72),(35,90),(36,61),(36,73),(36,90),(37,62),(37,74),(37,90),(38,63),(38,75),(38,90),(39,64),(39,76),(39,90),(40,65),(40,77),(40,90),(41,66),(41,72),(41,91),(42,67),(42,73),(42,91),(43,68),(43,74),(43,91),(44,69),(44,75),(44,91),(45,70),(45,76),(45,91),(46,71),(46,77),(46,91),(47,60),(47,62),(47,63),(47,78),(48,61),(48,62),(48,64),(48,79),(49,60),(49,61),(49,65),(49,80),(50,63),(50,64),(50,65),(50,81),(51,66),(51,68),(51,69),(51,78),(52,67),(52,68),(52,70),(52,79),(53,66),(53,67),(53,71),(53,80),(54,69),(54,70),(54,71),(54,81),(55,72),(55,74),(55,75),(55,78),(56,73),(56,74),(56,76),(56,79),(57,72),(57,73),(57,77),(57,80),(58,75),(58,76),(58,77),(58,81),(59,78),(59,79),(59,80),(59,81),(60,82),(60,94),(61,83),(61,94),(62,84),(62,94),(63,85),(63,94),(64,86),(64,94),(65,87),(65,94),(66,82),(66,92),(67,83),(67,92),(68,84),(68,92),(69,85),(69,92),(70,86),(70,92),(71,87),(71,92),(72,82),(72,93),(73,83),(73,93),(74,84),(74,93),(75,85),(75,93),(76,86),(76,93),(77,87),(77,93),(78,82),(78,84),(78,85),(79,83),(79,84),(79,86),(80,82),(80,83),(80,87),(81,85),(81,86),(81,87),(82,95),(83,95),(84,95),(85,95),(86,95),(87,95),(88,89),(88,90),(88,91),(89,92),(89,94),(90,93),(90,94),(91,92),(91,93),(92,95),(93,95),(94,95)],96)
 => ?
 => ? = 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,27),(8,28),(8,30),(8,45),(9,27),(9,29),(9,31),(9,46),(10,28),(10,29),(10,32),(10,47),(11,30),(11,31),(11,32),(11,48),(12,33),(12,34),(12,36),(12,45),(13,33),(13,35),(13,37),(13,46),(14,34),(14,35),(14,38),(14,47),(15,36),(15,37),(15,38),(15,48),(16,39),(16,40),(16,42),(16,45),(17,39),(17,41),(17,43),(17,46),(18,40),(18,41),(18,44),(18,47),(19,42),(19,43),(19,44),(19,48),(20,27),(20,33),(20,39),(20,55),(21,28),(21,34),(21,40),(21,55),(22,29),(22,35),(22,41),(22,55),(23,30),(23,36),(23,42),(23,55),(24,31),(24,37),(24,43),(24,55),(25,32),(25,38),(25,44),(25,55),(26,45),(26,46),(26,47),(26,48),(27,51),(27,56),(28,49),(28,56),(29,50),(29,56),(30,52),(30,56),(31,53),(31,56),(32,54),(32,56),(33,51),(33,57),(34,49),(34,57),(35,50),(35,57),(36,52),(36,57),(37,53),(37,57),(38,54),(38,57),(39,51),(39,58),(40,49),(40,58),(41,50),(41,58),(42,52),(42,58),(43,53),(43,58),(44,54),(44,58),(45,49),(45,51),(45,52),(46,50),(46,51),(46,53),(47,49),(47,50),(47,54),(48,52),(48,53),(48,54),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,56),(55,57),(55,58),(56,59),(57,59),(58,59)],60)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,27),(8,28),(8,30),(8,45),(9,27),(9,29),(9,31),(9,46),(10,28),(10,29),(10,32),(10,47),(11,30),(11,31),(11,32),(11,48),(12,33),(12,34),(12,36),(12,45),(13,33),(13,35),(13,37),(13,46),(14,34),(14,35),(14,38),(14,47),(15,36),(15,37),(15,38),(15,48),(16,39),(16,40),(16,42),(16,45),(17,39),(17,41),(17,43),(17,46),(18,40),(18,41),(18,44),(18,47),(19,42),(19,43),(19,44),(19,48),(20,27),(20,33),(20,39),(20,55),(21,28),(21,34),(21,40),(21,55),(22,29),(22,35),(22,41),(22,55),(23,30),(23,36),(23,42),(23,55),(24,31),(24,37),(24,43),(24,55),(25,32),(25,38),(25,44),(25,55),(26,45),(26,46),(26,47),(26,48),(27,51),(27,56),(28,49),(28,56),(29,50),(29,56),(30,52),(30,56),(31,53),(31,56),(32,54),(32,56),(33,51),(33,57),(34,49),(34,57),(35,50),(35,57),(36,52),(36,57),(37,53),(37,57),(38,54),(38,57),(39,51),(39,58),(40,49),(40,58),(41,50),(41,58),(42,52),(42,58),(43,53),(43,58),(44,54),(44,58),(45,49),(45,51),(45,52),(46,50),(46,51),(46,53),(47,49),(47,50),(47,54),(48,52),(48,53),(48,54),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,56),(55,57),(55,58),(56,59),(57,59),(58,59)],60)
 => ? = 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(1,15),(1,19),(1,23),(1,24),(1,25),(2,10),(2,14),(2,18),(2,21),(2,22),(2,25),(3,9),(3,13),(3,17),(3,20),(3,22),(3,24),(4,8),(4,12),(4,16),(4,20),(4,21),(4,23),(5,16),(5,17),(5,18),(5,19),(5,26),(6,12),(6,13),(6,14),(6,15),(6,26),(7,8),(7,9),(7,10),(7,11),(7,26),(8,31),(8,32),(8,34),(8,62),(9,31),(9,33),(9,35),(9,63),(10,32),(10,33),(10,36),(10,64),(11,34),(11,35),(11,36),(11,65),(12,37),(12,38),(12,40),(12,62),(13,37),(13,39),(13,41),(13,63),(14,38),(14,39),(14,42),(14,64),(15,40),(15,41),(15,42),(15,65),(16,43),(16,44),(16,46),(16,62),(17,43),(17,45),(17,47),(17,63),(18,44),(18,45),(18,48),(18,64),(19,46),(19,47),(19,48),(19,65),(20,27),(20,30),(20,31),(20,37),(20,43),(21,27),(21,28),(21,32),(21,38),(21,44),(22,27),(22,29),(22,33),(22,39),(22,45),(23,28),(23,30),(23,34),(23,40),(23,46),(24,29),(24,30),(24,35),(24,41),(24,47),(25,28),(25,29),(25,36),(25,42),(25,48),(26,62),(26,63),(26,64),(26,65),(27,49),(27,50),(27,54),(27,58),(28,49),(28,51),(28,55),(28,59),(29,49),(29,52),(29,56),(29,60),(30,49),(30,53),(30,57),(30,61),(31,50),(31,53),(31,68),(32,50),(32,51),(32,66),(33,50),(33,52),(33,67),(34,51),(34,53),(34,69),(35,52),(35,53),(35,70),(36,51),(36,52),(36,71),(37,54),(37,57),(37,68),(38,54),(38,55),(38,66),(39,54),(39,56),(39,67),(40,55),(40,57),(40,69),(41,56),(41,57),(41,70),(42,55),(42,56),(42,71),(43,58),(43,61),(43,68),(44,58),(44,59),(44,66),(45,58),(45,60),(45,67),(46,59),(46,61),(46,69),(47,60),(47,61),(47,70),(48,59),(48,60),(48,71),(49,72),(49,73),(49,74),(50,72),(50,78),(51,72),(51,75),(52,72),(52,76),(53,72),(53,77),(54,73),(54,78),(55,73),(55,75),(56,73),(56,76),(57,73),(57,77),(58,74),(58,78),(59,74),(59,75),(60,74),(60,76),(61,74),(61,77),(62,66),(62,68),(62,69),(63,67),(63,68),(63,70),(64,66),(64,67),(64,71),(65,69),(65,70),(65,71),(66,75),(66,78),(67,76),(67,78),(68,77),(68,78),(69,75),(69,77),(70,76),(70,77),(71,75),(71,76),(72,79),(73,79),(74,79),(75,79),(76,79),(77,79),(78,79)],80)
 => ?
 => ? = 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,16),(1,20),(1,27),(1,28),(1,29),(1,33),(2,11),(2,15),(2,19),(2,25),(2,26),(2,29),(2,32),(3,10),(3,14),(3,18),(3,24),(3,26),(3,28),(3,31),(4,9),(4,13),(4,17),(4,24),(4,25),(4,27),(4,30),(5,21),(5,22),(5,23),(5,30),(5,31),(5,32),(5,33),(6,17),(6,18),(6,19),(6,20),(6,23),(6,34),(7,13),(7,14),(7,15),(7,16),(7,22),(7,34),(8,9),(8,10),(8,11),(8,12),(8,21),(8,34),(9,41),(9,42),(9,44),(9,59),(9,89),(10,41),(10,43),(10,45),(10,60),(10,90),(11,42),(11,43),(11,46),(11,61),(11,91),(12,44),(12,45),(12,46),(12,62),(12,92),(13,47),(13,48),(13,50),(13,63),(13,89),(14,47),(14,49),(14,51),(14,64),(14,90),(15,48),(15,49),(15,52),(15,65),(15,91),(16,50),(16,51),(16,52),(16,66),(16,92),(17,53),(17,54),(17,56),(17,67),(17,89),(18,53),(18,55),(18,57),(18,68),(18,90),(19,54),(19,55),(19,58),(19,69),(19,91),(20,56),(20,57),(20,58),(20,70),(20,92),(21,59),(21,60),(21,61),(21,62),(21,93),(22,63),(22,64),(22,65),(22,66),(22,93),(23,67),(23,68),(23,69),(23,70),(23,93),(24,37),(24,41),(24,47),(24,53),(24,104),(25,35),(25,42),(25,48),(25,54),(25,104),(26,36),(26,43),(26,49),(26,55),(26,104),(27,38),(27,44),(27,50),(27,56),(27,104),(28,39),(28,45),(28,51),(28,57),(28,104),(29,40),(29,46),(29,52),(29,58),(29,104),(30,35),(30,37),(30,38),(30,59),(30,63),(30,67),(31,36),(31,37),(31,39),(31,60),(31,64),(31,68),(32,35),(32,36),(32,40),(32,61),(32,65),(32,69),(33,38),(33,39),(33,40),(33,62),(33,66),(33,70),(34,89),(34,90),(34,91),(34,92),(34,93),(35,71),(35,77),(35,83),(35,114),(36,72),(36,78),(36,84),(36,114),(37,73),(37,79),(37,85),(37,114),(38,74),(38,80),(38,86),(38,114),(39,75),(39,81),(39,87),(39,114),(40,76),(40,82),(40,88),(40,114),(41,73),(41,96),(41,111),(42,71),(42,94),(42,111),(43,72),(43,95),(43,111),(44,74),(44,97),(44,111),(45,75),(45,98),(45,111),(46,76),(46,99),(46,111),(47,79),(47,96),(47,112),(48,77),(48,94),(48,112),(49,78),(49,95),(49,112),(50,80),(50,97),(50,112),(51,81),(51,98),(51,112),(52,82),(52,99),(52,112),(53,85),(53,96),(53,113),(54,83),(54,94),(54,113),(55,84),(55,95),(55,113),(56,86),(56,97),(56,113),(57,87),(57,98),(57,113),(58,88),(58,99),(58,113),(59,71),(59,73),(59,74),(59,100),(60,72),(60,73),(60,75),(60,101),(61,71),(61,72),(61,76),(61,102),(62,74),(62,75),(62,76),(62,103),(63,77),(63,79),(63,80),(63,100),(64,78),(64,79),(64,81),(64,101),(65,77),(65,78),(65,82),(65,102),(66,80),(66,81),(66,82),(66,103),(67,83),(67,85),(67,86),(67,100),(68,84),(68,85),(68,87),(68,101),(69,83),(69,84),(69,88),(69,102),(70,86),(70,87),(70,88),(70,103),(71,105),(71,115),(72,106),(72,115),(73,107),(73,115),(74,108),(74,115),(75,109),(75,115),(76,110),(76,115),(77,105),(77,116),(78,106),(78,116),(79,107),(79,116),(80,108),(80,116),(81,109),(81,116),(82,110),(82,116),(83,105),(83,117),(84,106),(84,117),(85,107),(85,117),(86,108),(86,117),(87,109),(87,117),(88,110),(88,117),(89,94),(89,96),(89,97),(89,100),(90,95),(90,96),(90,98),(90,101),(91,94),(91,95),(91,99),(91,102),(92,97),(92,98),(92,99),(92,103),(93,100),(93,101),(93,102),(93,103),(94,105),(94,118),(95,106),(95,118),(96,107),(96,118),(97,108),(97,118),(98,109),(98,118),(99,110),(99,118),(100,105),(100,107),(100,108),(101,106),(101,107),(101,109),(102,105),(102,106),(102,110),(103,108),(103,109),(103,110),(104,111),(104,112),(104,113),(104,114),(105,119),(106,119),(107,119),(108,119),(109,119),(110,119),(111,115),(111,118),(112,116),(112,118),(113,117),(113,118),(114,115),(114,116),(114,117),(115,119),(116,119),(117,119),(118,119)],120)
 => ?
 => ? = 3
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,14),(4,15),(4,19),(4,20),(4,21),(4,60),(5,12),(5,13),(5,16),(5,17),(5,18),(5,60),(6,13),(6,15),(6,25),(6,26),(6,27),(6,59),(7,12),(7,14),(7,22),(7,23),(7,24),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,31),(9,32),(9,78),(9,81),(10,31),(10,33),(10,79),(10,82),(11,32),(11,33),(11,80),(11,83),(12,35),(12,36),(12,37),(12,94),(13,38),(13,39),(13,40),(13,94),(14,41),(14,42),(14,43),(14,94),(15,44),(15,45),(15,46),(15,94),(16,35),(16,38),(16,47),(16,48),(16,78),(17,36),(17,39),(17,47),(17,49),(17,79),(18,37),(18,40),(18,48),(18,49),(18,80),(19,41),(19,44),(19,50),(19,51),(19,78),(20,42),(20,45),(20,50),(20,52),(20,79),(21,43),(21,46),(21,51),(21,52),(21,80),(22,35),(22,41),(22,53),(22,54),(22,81),(23,36),(23,42),(23,53),(23,55),(23,82),(24,37),(24,43),(24,54),(24,55),(24,83),(25,38),(25,44),(25,56),(25,57),(25,81),(26,39),(26,45),(26,56),(26,58),(26,82),(27,40),(27,46),(27,57),(27,58),(27,83),(28,31),(28,34),(28,47),(28,50),(28,53),(28,56),(29,32),(29,34),(29,48),(29,51),(29,54),(29,57),(30,33),(30,34),(30,49),(30,52),(30,55),(30,58),(31,77),(31,86),(31,89),(32,77),(32,84),(32,87),(33,77),(33,85),(33,88),(34,73),(34,74),(34,75),(34,76),(34,77),(35,61),(35,62),(35,97),(36,61),(36,63),(36,98),(37,62),(37,63),(37,99),(38,64),(38,65),(38,97),(39,64),(39,66),(39,98),(40,65),(40,66),(40,99),(41,67),(41,68),(41,97),(42,67),(42,69),(42,98),(43,68),(43,69),(43,99),(44,70),(44,71),(44,97),(45,70),(45,72),(45,98),(46,71),(46,72),(46,99),(47,61),(47,64),(47,73),(47,86),(48,62),(48,65),(48,73),(48,84),(49,63),(49,66),(49,73),(49,85),(50,67),(50,70),(50,74),(50,86),(51,68),(51,71),(51,74),(51,84),(52,69),(52,72),(52,74),(52,85),(53,61),(53,67),(53,75),(53,89),(54,62),(54,68),(54,75),(54,87),(55,63),(55,69),(55,75),(55,88),(56,64),(56,70),(56,76),(56,89),(57,65),(57,71),(57,76),(57,87),(58,66),(58,72),(58,76),(58,88),(59,81),(59,82),(59,83),(59,94),(60,78),(60,79),(60,80),(60,94),(61,90),(61,102),(62,90),(62,100),(63,90),(63,101),(64,91),(64,102),(65,91),(65,100),(66,91),(66,101),(67,92),(67,102),(68,92),(68,100),(69,92),(69,101),(70,93),(70,102),(71,93),(71,100),(72,93),(72,101),(73,90),(73,91),(73,95),(74,92),(74,93),(74,95),(75,90),(75,92),(75,96),(76,91),(76,93),(76,96),(77,95),(77,96),(78,84),(78,86),(78,97),(79,85),(79,86),(79,98),(80,84),(80,85),(80,99),(81,87),(81,89),(81,97),(82,88),(82,89),(82,98),(83,87),(83,88),(83,99),(84,95),(84,100),(85,95),(85,101),(86,95),(86,102),(87,96),(87,100),(88,96),(88,101),(89,96),(89,102),(90,103),(91,103),(92,103),(93,103),(94,97),(94,98),(94,99),(95,103),(96,103),(97,100),(97,102),(98,101),(98,102),(99,100),(99,101),(100,103),(101,103),(102,103)],104)
 => ?
 => ? = 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
 => 1
Description
The number of minimal elements in a poset.
Matching statistic: St000771
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums 0, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). Its eigenvalues are 0,4,4,6, so the statistic is 2. The path on four vertices has eigenvalues 0, 4.7\dots, 6, 9.2\dots and therefore statistic 1.
Matching statistic: St000772
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums 0, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). Its eigenvalues are 0,4,4,6, so the statistic is 1. The path on four vertices has eigenvalues 0, 4.7\dots, 6, 9.2\dots and therefore also statistic 1. The graphs with statistic n-1, n-2 and n-3 have been characterised, see [1].
Matching statistic: St000777
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001645
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
Description
The pebbling number of a connected graph.
Matching statistic: St000259
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 4 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2 - 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 4 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2 - 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000302
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 22%●distinct values known / distinct values provided: 12%
Values
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 4 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ?
 => ? = 2 - 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 3 - 1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
Description
The determinant of the distance matrix of a connected graph.
The following 20 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000287The number of connected components of a graph. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001518The number of graphs with the same ordinary spectrum as the given graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000315The number of isolated vertices of a graph. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001488The number of corners of a skew partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St000264The girth of a graph, which is not a tree. St001060The distinguishing index of a graph. St001330The hat guessing number of a graph. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice.