Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001748
Mapping
St001748: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 1
['A',2]
 => 2
['B',2]
 => 7
['G',2]
 => 12
['A',3]
 => 7
['B',3]
 => 35
['C',3]
 => 35
['A',4]
 => 13
['B',4]
 => 111
['C',4]
 => 111
['D',4]
 => 51
['F',4]
 => 160
['A',5]
 => 34
['B',5]
 => 427
['C',5]
 => 427
['D',5]
 => 94
['A',6]
 => 72
['B',6]
 => 1303
['C',6]
 => 1303
['D',6]
 => 408
['E',6]
 => 166
['A',7]
 => 137
['B',7]
 => 4015
['C',7]
 => 4015
['D',7]
 => 960
['E',7]
 => 1096
['A',8]
 => 249
['B',8]
 => 9655
['C',8]
 => 9655
['D',8]
 => 2684
['E',8]
 => 3200
Description
The number of negative entries in the character table of the Weyl group of a Cartan type.
Matching statistic: St001765
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001765: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 12%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 7
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(1,9),(2,7),(2,9),(3,5),(3,8),(3,9),(4,6),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 35
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(1,9),(2,7),(2,9),(3,5),(3,8),(3,9),(4,6),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 35
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(0,10),(1,2),(1,7),(1,9),(1,10),(2,6),(2,8),(2,10),(3,4),(3,6),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,9),(8,10),(9,10)],11)
 => ? = 13
['B',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => ([(2,10),(3,6),(3,10),(3,13),(4,9),(4,11),(4,14),(4,15),(5,12),(5,13),(5,14),(5,15),(6,12),(6,14),(6,15),(7,8),(7,9),(7,12),(7,14),(7,15),(8,11),(8,13),(8,14),(8,15),(9,11),(9,13),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(11,15),(12,13),(13,14),(13,15)],16)
 => ([(0,16),(1,16),(2,10),(2,16),(3,6),(3,10),(3,13),(3,16),(4,9),(4,11),(4,14),(4,15),(4,16),(5,12),(5,13),(5,14),(5,15),(5,16),(6,12),(6,14),(6,15),(6,16),(7,8),(7,9),(7,12),(7,14),(7,15),(7,16),(8,11),(8,13),(8,14),(8,15),(8,16),(9,11),(9,13),(9,15),(9,16),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,13),(12,16),(13,14),(13,15),(13,16),(14,16),(15,16)],17)
 => ? = 111
['C',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => ([(2,10),(3,6),(3,10),(3,13),(4,9),(4,11),(4,14),(4,15),(5,12),(5,13),(5,14),(5,15),(6,12),(6,14),(6,15),(7,8),(7,9),(7,12),(7,14),(7,15),(8,11),(8,13),(8,14),(8,15),(9,11),(9,13),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(11,15),(12,13),(13,14),(13,15)],16)
 => ([(0,16),(1,16),(2,10),(2,16),(3,6),(3,10),(3,13),(3,16),(4,9),(4,11),(4,14),(4,15),(4,16),(5,12),(5,13),(5,14),(5,15),(5,16),(6,12),(6,14),(6,15),(6,16),(7,8),(7,9),(7,12),(7,14),(7,15),(7,16),(8,11),(8,13),(8,14),(8,15),(8,16),(9,11),(9,13),(9,15),(9,16),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,13),(12,16),(13,14),(13,15),(13,16),(14,16),(15,16)],17)
 => ? = 111
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => ([(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,11),(4,5),(4,7),(4,10),(5,6),(5,9),(6,7),(6,8),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
 => ([(0,12),(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,5),(3,8),(3,11),(3,12),(4,5),(4,7),(4,10),(4,12),(5,6),(5,9),(5,12),(6,7),(6,8),(6,10),(6,11),(6,12),(7,8),(7,9),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 51
['F',4]
 => ([(0,18),(1,19),(2,18),(2,22),(3,19),(3,22),(4,6),(6,5),(7,11),(8,16),(9,17),(10,13),(10,14),(11,4),(12,23),(13,8),(13,23),(14,9),(14,23),(15,11),(16,15),(17,7),(17,15),(18,20),(19,21),(20,12),(20,13),(21,12),(21,14),(22,10),(22,20),(22,21),(23,16),(23,17)],24)
 => ([(4,8),(5,20),(5,23),(6,7),(6,23),(7,8),(7,20),(8,23),(9,18),(9,19),(9,21),(9,22),(10,11),(10,18),(10,21),(10,22),(11,19),(11,21),(11,22),(12,15),(12,16),(12,17),(12,20),(12,23),(13,14),(13,16),(13,17),(13,19),(13,22),(13,23),(14,15),(14,17),(14,18),(14,20),(14,21),(15,16),(15,19),(15,22),(15,23),(16,18),(16,20),(16,21),(17,18),(17,19),(17,21),(17,22),(18,19),(18,22),(18,23),(19,20),(19,21),(20,22),(20,23),(21,22),(21,23)],24)
 => ([(0,24),(1,24),(2,24),(3,24),(4,8),(4,24),(5,20),(5,23),(5,24),(6,7),(6,23),(6,24),(7,8),(7,20),(7,24),(8,23),(8,24),(9,18),(9,19),(9,21),(9,22),(9,24),(10,11),(10,18),(10,21),(10,22),(10,24),(11,19),(11,21),(11,22),(11,24),(12,15),(12,16),(12,17),(12,20),(12,23),(12,24),(13,14),(13,16),(13,17),(13,19),(13,22),(13,23),(13,24),(14,15),(14,17),(14,18),(14,20),(14,21),(14,24),(15,16),(15,19),(15,22),(15,23),(15,24),(16,18),(16,20),(16,21),(16,24),(17,18),(17,19),(17,21),(17,22),(17,24),(18,19),(18,22),(18,23),(18,24),(19,20),(19,21),(19,24),(20,22),(20,23),(20,24),(21,22),(21,23),(21,24),(22,24),(23,24)],25)
 => ? = 160
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(0,15),(1,2),(1,10),(1,12),(1,14),(1,15),(2,9),(2,11),(2,13),(2,15),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(3,15),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(5,15),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(6,15),(7,8),(7,9),(7,11),(7,13),(7,14),(7,15),(8,10),(8,12),(8,13),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,13),(10,15),(11,12),(11,14),(11,15),(12,13),(12,15),(13,14),(13,15),(14,15)],16)
 => ? = 34
['B',5]
 => ([(0,18),(1,17),(2,18),(2,24),(3,23),(3,24),(4,17),(4,23),(6,15),(7,16),(8,9),(9,5),(10,12),(11,13),(12,11),(13,14),(14,9),(15,7),(15,21),(16,8),(16,14),(17,10),(18,6),(18,19),(19,15),(19,22),(20,12),(20,22),(21,13),(21,16),(22,11),(22,21),(23,10),(23,20),(24,19),(24,20)],25)
 => ([(2,10),(3,6),(3,10),(3,20),(4,5),(4,19),(4,20),(4,22),(4,23),(4,24),(5,6),(5,10),(5,15),(5,20),(5,21),(6,19),(6,22),(6,23),(6,24),(7,15),(7,19),(7,20),(7,21),(7,22),(7,23),(7,24),(8,9),(8,16),(8,17),(8,18),(8,22),(8,23),(8,24),(9,14),(9,16),(9,17),(9,21),(9,23),(9,24),(10,19),(10,22),(10,23),(10,24),(11,14),(11,16),(11,17),(11,18),(11,21),(11,22),(11,23),(11,24),(12,13),(12,17),(12,18),(12,19),(12,21),(12,22),(12,23),(12,24),(13,14),(13,15),(13,16),(13,20),(13,21),(13,22),(13,23),(13,24),(14,17),(14,18),(14,19),(14,22),(14,23),(14,24),(15,17),(15,18),(15,19),(15,22),(15,23),(15,24),(16,17),(16,18),(16,19),(16,22),(16,23),(16,24),(17,20),(17,21),(17,24),(18,20),(18,21),(18,23),(18,24),(19,20),(19,21),(20,22),(20,23),(20,24),(21,22),(21,23),(21,24)],25)
 => ([(0,25),(1,25),(2,10),(2,25),(3,6),(3,10),(3,20),(3,25),(4,5),(4,19),(4,20),(4,22),(4,23),(4,24),(4,25),(5,6),(5,10),(5,15),(5,20),(5,21),(5,25),(6,19),(6,22),(6,23),(6,24),(6,25),(7,15),(7,19),(7,20),(7,21),(7,22),(7,23),(7,24),(7,25),(8,9),(8,16),(8,17),(8,18),(8,22),(8,23),(8,24),(8,25),(9,14),(9,16),(9,17),(9,21),(9,23),(9,24),(9,25),(10,19),(10,22),(10,23),(10,24),(10,25),(11,14),(11,16),(11,17),(11,18),(11,21),(11,22),(11,23),(11,24),(11,25),(12,13),(12,17),(12,18),(12,19),(12,21),(12,22),(12,23),(12,24),(12,25),(13,14),(13,15),(13,16),(13,20),(13,21),(13,22),(13,23),(13,24),(13,25),(14,17),(14,18),(14,19),(14,22),(14,23),(14,24),(14,25),(15,17),(15,18),(15,19),(15,22),(15,23),(15,24),(15,25),(16,17),(16,18),(16,19),(16,22),(16,23),(16,24),(16,25),(17,20),(17,21),(17,24),(17,25),(18,20),(18,21),(18,23),(18,24),(18,25),(19,20),(19,21),(19,25),(20,22),(20,23),(20,24),(20,25),(21,22),(21,23),(21,24),(21,25),(22,25),(23,25),(24,25)],26)
 => ? = 427
['C',5]
 => ([(0,18),(1,17),(2,18),(2,24),(3,23),(3,24),(4,17),(4,23),(6,15),(7,16),(8,9),(9,5),(10,12),(11,13),(12,11),(13,14),(14,9),(15,7),(15,21),(16,8),(16,14),(17,10),(18,6),(18,19),(19,15),(19,22),(20,12),(20,22),(21,13),(21,16),(22,11),(22,21),(23,10),(23,20),(24,19),(24,20)],25)
 => ([(2,10),(3,6),(3,10),(3,20),(4,5),(4,19),(4,20),(4,22),(4,23),(4,24),(5,6),(5,10),(5,15),(5,20),(5,21),(6,19),(6,22),(6,23),(6,24),(7,15),(7,19),(7,20),(7,21),(7,22),(7,23),(7,24),(8,9),(8,16),(8,17),(8,18),(8,22),(8,23),(8,24),(9,14),(9,16),(9,17),(9,21),(9,23),(9,24),(10,19),(10,22),(10,23),(10,24),(11,14),(11,16),(11,17),(11,18),(11,21),(11,22),(11,23),(11,24),(12,13),(12,17),(12,18),(12,19),(12,21),(12,22),(12,23),(12,24),(13,14),(13,15),(13,16),(13,20),(13,21),(13,22),(13,23),(13,24),(14,17),(14,18),(14,19),(14,22),(14,23),(14,24),(15,17),(15,18),(15,19),(15,22),(15,23),(15,24),(16,17),(16,18),(16,19),(16,22),(16,23),(16,24),(17,20),(17,21),(17,24),(18,20),(18,21),(18,23),(18,24),(19,20),(19,21),(20,22),(20,23),(20,24),(21,22),(21,23),(21,24)],25)
 => ([(0,25),(1,25),(2,10),(2,25),(3,6),(3,10),(3,20),(3,25),(4,5),(4,19),(4,20),(4,22),(4,23),(4,24),(4,25),(5,6),(5,10),(5,15),(5,20),(5,21),(5,25),(6,19),(6,22),(6,23),(6,24),(6,25),(7,15),(7,19),(7,20),(7,21),(7,22),(7,23),(7,24),(7,25),(8,9),(8,16),(8,17),(8,18),(8,22),(8,23),(8,24),(8,25),(9,14),(9,16),(9,17),(9,21),(9,23),(9,24),(9,25),(10,19),(10,22),(10,23),(10,24),(10,25),(11,14),(11,16),(11,17),(11,18),(11,21),(11,22),(11,23),(11,24),(11,25),(12,13),(12,17),(12,18),(12,19),(12,21),(12,22),(12,23),(12,24),(12,25),(13,14),(13,15),(13,16),(13,20),(13,21),(13,22),(13,23),(13,24),(13,25),(14,17),(14,18),(14,19),(14,22),(14,23),(14,24),(14,25),(15,17),(15,18),(15,19),(15,22),(15,23),(15,24),(15,25),(16,17),(16,18),(16,19),(16,22),(16,23),(16,24),(16,25),(17,20),(17,21),(17,24),(17,25),(18,20),(18,21),(18,23),(18,24),(18,25),(19,20),(19,21),(19,25),(20,22),(20,23),(20,24),(20,25),(21,22),(21,23),(21,24),(21,25),(22,25),(23,25),(24,25)],26)
 => ? = 427
['D',5]
 => ([(0,13),(1,16),(2,15),(3,13),(3,17),(4,15),(4,16),(4,17),(6,10),(7,19),(8,19),(9,18),(10,5),(11,7),(11,18),(12,8),(12,18),(13,14),(14,7),(14,8),(15,9),(15,11),(16,9),(16,12),(17,11),(17,12),(17,14),(18,6),(18,19),(19,10)],20)
 => ([(2,5),(3,8),(3,9),(3,15),(3,18),(3,19),(4,7),(4,16),(4,17),(4,18),(4,19),(5,8),(5,9),(5,15),(5,18),(5,19),(6,12),(6,13),(6,14),(6,16),(6,17),(6,18),(6,19),(7,12),(7,13),(7,14),(7,16),(7,17),(7,19),(8,9),(8,11),(8,13),(8,14),(8,17),(9,10),(9,12),(9,14),(9,16),(10,11),(10,13),(10,14),(10,15),(10,17),(10,18),(10,19),(11,12),(11,14),(11,15),(11,16),(11,18),(11,19),(12,13),(12,15),(12,17),(12,18),(12,19),(13,15),(13,16),(13,18),(13,19),(14,15),(14,18),(14,19),(15,16),(15,17),(16,17),(16,18),(16,19),(17,18),(17,19)],20)
 => ([(0,20),(1,20),(2,5),(2,20),(3,8),(3,9),(3,15),(3,18),(3,19),(3,20),(4,7),(4,16),(4,17),(4,18),(4,19),(4,20),(5,8),(5,9),(5,15),(5,18),(5,19),(5,20),(6,12),(6,13),(6,14),(6,16),(6,17),(6,18),(6,19),(6,20),(7,12),(7,13),(7,14),(7,16),(7,17),(7,19),(7,20),(8,9),(8,11),(8,13),(8,14),(8,17),(8,20),(9,10),(9,12),(9,14),(9,16),(9,20),(10,11),(10,13),(10,14),(10,15),(10,17),(10,18),(10,19),(10,20),(11,12),(11,14),(11,15),(11,16),(11,18),(11,19),(11,20),(12,13),(12,15),(12,17),(12,18),(12,19),(12,20),(13,15),(13,16),(13,18),(13,19),(13,20),(14,15),(14,18),(14,19),(14,20),(15,16),(15,17),(15,20),(16,17),(16,18),(16,19),(16,20),(17,18),(17,19),(17,20),(18,20),(19,20)],21)
 => ? = 94
['A',6]
 => ([(0,14),(1,13),(2,18),(2,20),(3,19),(3,20),(4,13),(4,18),(5,14),(5,19),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,17),(16,10),(16,17),(17,11),(17,12),(18,7),(18,15),(19,8),(19,16),(20,15),(20,16)],21)
 => ([(1,2),(1,7),(1,16),(1,18),(1,20),(2,6),(2,15),(2,17),(2,19),(3,6),(3,7),(3,15),(3,16),(3,17),(3,18),(3,19),(3,20),(4,5),(4,11),(4,12),(4,14),(4,15),(4,17),(4,18),(4,19),(4,20),(5,11),(5,12),(5,13),(5,16),(5,17),(5,18),(5,19),(5,20),(6,7),(6,9),(6,11),(6,13),(6,16),(6,18),(6,20),(7,10),(7,12),(7,14),(7,15),(7,17),(7,19),(8,11),(8,12),(8,13),(8,14),(8,15),(8,16),(8,17),(8,18),(8,19),(8,20),(9,10),(9,12),(9,14),(9,15),(9,16),(9,17),(9,18),(9,19),(9,20),(10,11),(10,13),(10,15),(10,16),(10,17),(10,18),(10,19),(10,20),(11,12),(11,14),(11,15),(11,17),(11,19),(11,20),(12,13),(12,16),(12,18),(12,19),(12,20),(13,14),(13,15),(13,17),(13,18),(13,19),(13,20),(14,16),(14,17),(14,18),(14,19),(14,20),(15,16),(15,18),(15,20),(16,17),(16,19),(17,18),(17,20),(18,19),(19,20)],21)
 => ([(0,21),(1,2),(1,7),(1,16),(1,18),(1,20),(1,21),(2,6),(2,15),(2,17),(2,19),(2,21),(3,6),(3,7),(3,15),(3,16),(3,17),(3,18),(3,19),(3,20),(3,21),(4,5),(4,11),(4,12),(4,14),(4,15),(4,17),(4,18),(4,19),(4,20),(4,21),(5,11),(5,12),(5,13),(5,16),(5,17),(5,18),(5,19),(5,20),(5,21),(6,7),(6,9),(6,11),(6,13),(6,16),(6,18),(6,20),(6,21),(7,10),(7,12),(7,14),(7,15),(7,17),(7,19),(7,21),(8,11),(8,12),(8,13),(8,14),(8,15),(8,16),(8,17),(8,18),(8,19),(8,20),(8,21),(9,10),(9,12),(9,14),(9,15),(9,16),(9,17),(9,18),(9,19),(9,20),(9,21),(10,11),(10,13),(10,15),(10,16),(10,17),(10,18),(10,19),(10,20),(10,21),(11,12),(11,14),(11,15),(11,17),(11,19),(11,20),(11,21),(12,13),(12,16),(12,18),(12,19),(12,20),(12,21),(13,14),(13,15),(13,17),(13,18),(13,19),(13,20),(13,21),(14,16),(14,17),(14,18),(14,19),(14,20),(14,21),(15,16),(15,18),(15,20),(15,21),(16,17),(16,19),(16,21),(17,18),(17,20),(17,21),(18,19),(18,21),(19,20),(19,21),(20,21)],22)
 => ? = 72
['B',6]
 => ([(0,23),(1,22),(2,23),(2,34),(3,33),(3,34),(4,33),(4,35),(5,22),(5,35),(7,20),(8,19),(9,21),(10,11),(11,6),(12,16),(13,15),(14,13),(15,17),(16,14),(17,18),(18,11),(19,9),(19,27),(20,8),(20,28),(21,10),(21,18),(22,12),(23,7),(23,24),(24,20),(24,32),(25,16),(25,31),(26,31),(26,32),(27,17),(27,21),(28,19),(28,29),(29,15),(29,27),(30,13),(30,29),(31,14),(31,30),(32,28),(32,30),(33,25),(33,26),(34,24),(34,26),(35,12),(35,25)],36)
 => ([(2,8),(3,6),(3,8),(3,26),(4,5),(4,6),(4,8),(4,20),(4,26),(4,31),(5,10),(5,25),(5,26),(5,32),(5,33),(5,34),(5,35),(6,10),(6,25),(6,32),(6,33),(6,34),(6,35),(7,10),(7,20),(7,25),(7,26),(7,31),(7,32),(7,33),(7,34),(7,35),(8,10),(8,25),(8,32),(8,33),(8,34),(8,35),(9,12),(9,16),(9,22),(9,24),(9,28),(9,29),(9,30),(9,33),(9,34),(9,35),(10,15),(10,20),(10,23),(10,26),(10,30),(10,31),(11,15),(11,20),(11,23),(11,25),(11,26),(11,30),(11,31),(11,32),(11,33),(11,34),(11,35),(12,16),(12,17),(12,24),(12,27),(12,28),(12,29),(12,32),(12,33),(12,34),(12,35),(13,21),(13,23),(13,25),(13,27),(13,28),(13,29),(13,30),(13,31),(13,32),(13,33),(13,34),(13,35),(14,16),(14,17),(14,22),(14,24),(14,27),(14,28),(14,29),(14,30),(14,32),(14,33),(14,34),(14,35),(15,21),(15,25),(15,27),(15,28),(15,29),(15,31),(15,32),(15,33),(15,34),(15,35),(16,19),(16,22),(16,23),(16,24),(16,28),(16,30),(16,31),(16,34),(16,35),(17,19),(17,22),(17,23),(17,24),(17,28),(17,29),(17,30),(17,31),(17,33),(17,34),(17,35),(18,19),(18,22),(18,23),(18,24),(18,27),(18,28),(18,29),(18,30),(18,31),(18,32),(18,33),(18,34),(18,35),(19,21),(19,25),(19,27),(19,28),(19,29),(19,30),(19,32),(19,33),(19,34),(19,35),(20,21),(20,25),(20,27),(20,28),(20,29),(20,32),(20,33),(20,34),(20,35),(21,22),(21,23),(21,24),(21,26),(21,30),(21,31),(21,32),(21,33),(21,34),(21,35),(22,25),(22,27),(22,28),(22,29),(22,32),(22,33),(22,34),(22,35),(23,25),(23,27),(23,28),(23,29),(23,32),(23,33),(23,34),(23,35),(24,25),(24,27),(24,28),(24,29),(24,32),(24,33),(24,34),(24,35),(25,26),(25,30),(25,31),(26,27),(26,28),(26,29),(26,32),(26,33),(26,34),(26,35),(27,30),(27,31),(27,33),(27,34),(27,35),(28,30),(28,31),(28,35),(29,30),(29,31),(29,34),(29,35),(30,32),(30,33),(30,34),(30,35),(31,32),(31,33),(31,34),(31,35)],36)
 => ([(0,36),(1,36),(2,8),(2,36),(3,6),(3,8),(3,26),(3,36),(4,5),(4,6),(4,8),(4,20),(4,26),(4,31),(4,36),(5,10),(5,25),(5,26),(5,32),(5,33),(5,34),(5,35),(5,36),(6,10),(6,25),(6,32),(6,33),(6,34),(6,35),(6,36),(7,10),(7,20),(7,25),(7,26),(7,31),(7,32),(7,33),(7,34),(7,35),(7,36),(8,10),(8,25),(8,32),(8,33),(8,34),(8,35),(8,36),(9,12),(9,16),(9,22),(9,24),(9,28),(9,29),(9,30),(9,33),(9,34),(9,35),(9,36),(10,15),(10,20),(10,23),(10,26),(10,30),(10,31),(10,36),(11,15),(11,20),(11,23),(11,25),(11,26),(11,30),(11,31),(11,32),(11,33),(11,34),(11,35),(11,36),(12,16),(12,17),(12,24),(12,27),(12,28),(12,29),(12,32),(12,33),(12,34),(12,35),(12,36),(13,21),(13,23),(13,25),(13,27),(13,28),(13,29),(13,30),(13,31),(13,32),(13,33),(13,34),(13,35),(13,36),(14,16),(14,17),(14,22),(14,24),(14,27),(14,28),(14,29),(14,30),(14,32),(14,33),(14,34),(14,35),(14,36),(15,21),(15,25),(15,27),(15,28),(15,29),(15,31),(15,32),(15,33),(15,34),(15,35),(15,36),(16,19),(16,22),(16,23),(16,24),(16,28),(16,30),(16,31),(16,34),(16,35),(16,36),(17,19),(17,22),(17,23),(17,24),(17,28),(17,29),(17,30),(17,31),(17,33),(17,34),(17,35),(17,36),(18,19),(18,22),(18,23),(18,24),(18,27),(18,28),(18,29),(18,30),(18,31),(18,32),(18,33),(18,34),(18,35),(18,36),(19,21),(19,25),(19,27),(19,28),(19,29),(19,30),(19,32),(19,33),(19,34),(19,35),(19,36),(20,21),(20,25),(20,27),(20,28),(20,29),(20,32),(20,33),(20,34),(20,35),(20,36),(21,22),(21,23),(21,24),(21,26),(21,30),(21,31),(21,32),(21,33),(21,34),(21,35),(21,36),(22,25),(22,27),(22,28),(22,29),(22,32),(22,33),(22,34),(22,35),(22,36),(23,25),(23,27),(23,28),(23,29),(23,32),(23,33),(23,34),(23,35),(23,36),(24,25),(24,27),(24,28),(24,29),(24,32),(24,33),(24,34),(24,35),(24,36),(25,26),(25,30),(25,31),(25,36),(26,27),(26,28),(26,29),(26,32),(26,33),(26,34),(26,35),(26,36),(27,30),(27,31),(27,33),(27,34),(27,35),(27,36),(28,30),(28,31),(28,35),(28,36),(29,30),(29,31),(29,34),(29,35),(29,36),(30,32),(30,33),(30,34),(30,35),(30,36),(31,32),(31,33),(31,34),(31,35),(31,36),(32,36),(33,36),(34,36),(35,36)],37)
 => ? = 1303
['C',6]
 => ([(0,23),(1,22),(2,23),(2,34),(3,33),(3,34),(4,33),(4,35),(5,22),(5,35),(7,20),(8,19),(9,21),(10,11),(11,6),(12,16),(13,15),(14,13),(15,17),(16,14),(17,18),(18,11),(19,9),(19,27),(20,8),(20,28),(21,10),(21,18),(22,12),(23,7),(23,24),(24,20),(24,32),(25,16),(25,31),(26,31),(26,32),(27,17),(27,21),(28,19),(28,29),(29,15),(29,27),(30,13),(30,29),(31,14),(31,30),(32,28),(32,30),(33,25),(33,26),(34,24),(34,26),(35,12),(35,25)],36)
 => ([(2,8),(3,6),(3,8),(3,26),(4,5),(4,6),(4,8),(4,20),(4,26),(4,31),(5,10),(5,25),(5,26),(5,32),(5,33),(5,34),(5,35),(6,10),(6,25),(6,32),(6,33),(6,34),(6,35),(7,10),(7,20),(7,25),(7,26),(7,31),(7,32),(7,33),(7,34),(7,35),(8,10),(8,25),(8,32),(8,33),(8,34),(8,35),(9,12),(9,16),(9,22),(9,24),(9,28),(9,29),(9,30),(9,33),(9,34),(9,35),(10,15),(10,20),(10,23),(10,26),(10,30),(10,31),(11,15),(11,20),(11,23),(11,25),(11,26),(11,30),(11,31),(11,32),(11,33),(11,34),(11,35),(12,16),(12,17),(12,24),(12,27),(12,28),(12,29),(12,32),(12,33),(12,34),(12,35),(13,21),(13,23),(13,25),(13,27),(13,28),(13,29),(13,30),(13,31),(13,32),(13,33),(13,34),(13,35),(14,16),(14,17),(14,22),(14,24),(14,27),(14,28),(14,29),(14,30),(14,32),(14,33),(14,34),(14,35),(15,21),(15,25),(15,27),(15,28),(15,29),(15,31),(15,32),(15,33),(15,34),(15,35),(16,19),(16,22),(16,23),(16,24),(16,28),(16,30),(16,31),(16,34),(16,35),(17,19),(17,22),(17,23),(17,24),(17,28),(17,29),(17,30),(17,31),(17,33),(17,34),(17,35),(18,19),(18,22),(18,23),(18,24),(18,27),(18,28),(18,29),(18,30),(18,31),(18,32),(18,33),(18,34),(18,35),(19,21),(19,25),(19,27),(19,28),(19,29),(19,30),(19,32),(19,33),(19,34),(19,35),(20,21),(20,25),(20,27),(20,28),(20,29),(20,32),(20,33),(20,34),(20,35),(21,22),(21,23),(21,24),(21,26),(21,30),(21,31),(21,32),(21,33),(21,34),(21,35),(22,25),(22,27),(22,28),(22,29),(22,32),(22,33),(22,34),(22,35),(23,25),(23,27),(23,28),(23,29),(23,32),(23,33),(23,34),(23,35),(24,25),(24,27),(24,28),(24,29),(24,32),(24,33),(24,34),(24,35),(25,26),(25,30),(25,31),(26,27),(26,28),(26,29),(26,32),(26,33),(26,34),(26,35),(27,30),(27,31),(27,33),(27,34),(27,35),(28,30),(28,31),(28,35),(29,30),(29,31),(29,34),(29,35),(30,32),(30,33),(30,34),(30,35),(31,32),(31,33),(31,34),(31,35)],36)
 => ([(0,36),(1,36),(2,8),(2,36),(3,6),(3,8),(3,26),(3,36),(4,5),(4,6),(4,8),(4,20),(4,26),(4,31),(4,36),(5,10),(5,25),(5,26),(5,32),(5,33),(5,34),(5,35),(5,36),(6,10),(6,25),(6,32),(6,33),(6,34),(6,35),(6,36),(7,10),(7,20),(7,25),(7,26),(7,31),(7,32),(7,33),(7,34),(7,35),(7,36),(8,10),(8,25),(8,32),(8,33),(8,34),(8,35),(8,36),(9,12),(9,16),(9,22),(9,24),(9,28),(9,29),(9,30),(9,33),(9,34),(9,35),(9,36),(10,15),(10,20),(10,23),(10,26),(10,30),(10,31),(10,36),(11,15),(11,20),(11,23),(11,25),(11,26),(11,30),(11,31),(11,32),(11,33),(11,34),(11,35),(11,36),(12,16),(12,17),(12,24),(12,27),(12,28),(12,29),(12,32),(12,33),(12,34),(12,35),(12,36),(13,21),(13,23),(13,25),(13,27),(13,28),(13,29),(13,30),(13,31),(13,32),(13,33),(13,34),(13,35),(13,36),(14,16),(14,17),(14,22),(14,24),(14,27),(14,28),(14,29),(14,30),(14,32),(14,33),(14,34),(14,35),(14,36),(15,21),(15,25),(15,27),(15,28),(15,29),(15,31),(15,32),(15,33),(15,34),(15,35),(15,36),(16,19),(16,22),(16,23),(16,24),(16,28),(16,30),(16,31),(16,34),(16,35),(16,36),(17,19),(17,22),(17,23),(17,24),(17,28),(17,29),(17,30),(17,31),(17,33),(17,34),(17,35),(17,36),(18,19),(18,22),(18,23),(18,24),(18,27),(18,28),(18,29),(18,30),(18,31),(18,32),(18,33),(18,34),(18,35),(18,36),(19,21),(19,25),(19,27),(19,28),(19,29),(19,30),(19,32),(19,33),(19,34),(19,35),(19,36),(20,21),(20,25),(20,27),(20,28),(20,29),(20,32),(20,33),(20,34),(20,35),(20,36),(21,22),(21,23),(21,24),(21,26),(21,30),(21,31),(21,32),(21,33),(21,34),(21,35),(21,36),(22,25),(22,27),(22,28),(22,29),(22,32),(22,33),(22,34),(22,35),(22,36),(23,25),(23,27),(23,28),(23,29),(23,32),(23,33),(23,34),(23,35),(23,36),(24,25),(24,27),(24,28),(24,29),(24,32),(24,33),(24,34),(24,35),(24,36),(25,26),(25,30),(25,31),(25,36),(26,27),(26,28),(26,29),(26,32),(26,33),(26,34),(26,35),(26,36),(27,30),(27,31),(27,33),(27,34),(27,35),(27,36),(28,30),(28,31),(28,35),(28,36),(29,30),(29,31),(29,34),(29,35),(29,36),(30,32),(30,33),(30,34),(30,35),(30,36),(31,32),(31,33),(31,34),(31,35),(31,36),(32,36),(33,36),(34,36),(35,36)],37)
 => ? = 1303
['D',6]
 => ([(0,24),(1,23),(2,20),(3,22),(3,26),(4,20),(4,22),(5,23),(5,24),(5,26),(7,12),(8,19),(9,27),(10,29),(11,29),(12,6),(13,16),(13,27),(14,17),(14,27),(15,21),(16,10),(16,28),(17,11),(17,28),(18,12),(19,7),(19,18),(20,15),(21,10),(21,11),(22,15),(22,25),(23,9),(23,13),(24,9),(24,14),(25,16),(25,17),(25,21),(26,13),(26,14),(26,25),(27,8),(27,28),(28,19),(28,29),(29,18)],30)
 => ([(2,7),(3,5),(3,7),(3,20),(4,11),(4,12),(4,20),(4,23),(4,27),(4,28),(4,29),(5,11),(5,12),(5,23),(5,27),(5,28),(5,29),(6,8),(6,18),(6,19),(6,25),(6,26),(6,27),(6,28),(6,29),(7,11),(7,12),(7,23),(7,27),(7,28),(7,29),(8,19),(8,21),(8,22),(8,24),(8,25),(8,26),(8,28),(8,29),(9,18),(9,19),(9,21),(9,22),(9,24),(9,25),(9,26),(9,27),(9,28),(9,29),(10,11),(10,12),(10,13),(10,14),(10,15),(10,18),(10,19),(10,23),(10,27),(10,28),(10,29),(11,12),(11,15),(11,17),(11,20),(11,22),(11,24),(11,26),(12,14),(12,16),(12,20),(12,21),(12,24),(12,25),(13,16),(13,17),(13,20),(13,21),(13,22),(13,24),(13,25),(13,26),(13,27),(13,28),(13,29),(14,15),(14,17),(14,20),(14,22),(14,23),(14,24),(14,26),(14,27),(14,28),(14,29),(15,16),(15,20),(15,21),(15,23),(15,24),(15,25),(15,27),(15,28),(15,29),(16,17),(16,18),(16,19),(16,22),(16,23),(16,24),(16,26),(16,27),(16,28),(16,29),(17,18),(17,19),(17,21),(17,23),(17,24),(17,25),(17,27),(17,28),(17,29),(18,20),(18,21),(18,22),(18,24),(18,25),(18,26),(18,28),(18,29),(19,20),(19,21),(19,22),(19,24),(19,25),(19,26),(19,29),(20,23),(20,27),(20,28),(20,29),(21,22),(21,23),(21,26),(21,27),(21,28),(21,29),(22,23),(22,25),(22,27),(22,28),(22,29),(23,24),(23,25),(23,26),(24,27),(24,28),(24,29),(25,26),(25,27),(25,28),(25,29),(26,27),(26,28),(26,29)],30)
 => ([(0,30),(1,30),(2,7),(2,30),(3,5),(3,7),(3,20),(3,30),(4,11),(4,12),(4,20),(4,23),(4,27),(4,28),(4,29),(4,30),(5,11),(5,12),(5,23),(5,27),(5,28),(5,29),(5,30),(6,8),(6,18),(6,19),(6,25),(6,26),(6,27),(6,28),(6,29),(6,30),(7,11),(7,12),(7,23),(7,27),(7,28),(7,29),(7,30),(8,19),(8,21),(8,22),(8,24),(8,25),(8,26),(8,28),(8,29),(8,30),(9,18),(9,19),(9,21),(9,22),(9,24),(9,25),(9,26),(9,27),(9,28),(9,29),(9,30),(10,11),(10,12),(10,13),(10,14),(10,15),(10,18),(10,19),(10,23),(10,27),(10,28),(10,29),(10,30),(11,12),(11,15),(11,17),(11,20),(11,22),(11,24),(11,26),(11,30),(12,14),(12,16),(12,20),(12,21),(12,24),(12,25),(12,30),(13,16),(13,17),(13,20),(13,21),(13,22),(13,24),(13,25),(13,26),(13,27),(13,28),(13,29),(13,30),(14,15),(14,17),(14,20),(14,22),(14,23),(14,24),(14,26),(14,27),(14,28),(14,29),(14,30),(15,16),(15,20),(15,21),(15,23),(15,24),(15,25),(15,27),(15,28),(15,29),(15,30),(16,17),(16,18),(16,19),(16,22),(16,23),(16,24),(16,26),(16,27),(16,28),(16,29),(16,30),(17,18),(17,19),(17,21),(17,23),(17,24),(17,25),(17,27),(17,28),(17,29),(17,30),(18,20),(18,21),(18,22),(18,24),(18,25),(18,26),(18,28),(18,29),(18,30),(19,20),(19,21),(19,22),(19,24),(19,25),(19,26),(19,29),(19,30),(20,23),(20,27),(20,28),(20,29),(20,30),(21,22),(21,23),(21,26),(21,27),(21,28),(21,29),(21,30),(22,23),(22,25),(22,27),(22,28),(22,29),(22,30),(23,24),(23,25),(23,26),(23,30),(24,27),(24,28),(24,29),(24,30),(25,26),(25,27),(25,28),(25,29),(25,30),(26,27),(26,28),(26,29),(26,30),(27,30),(28,30),(29,30)],31)
 => ? = 408
['E',6]
 => ([(0,28),(1,24),(2,23),(3,23),(3,29),(4,24),(4,30),(5,28),(5,29),(5,30),(6,7),(8,19),(9,20),(10,14),(10,15),(11,34),(12,32),(13,33),(14,8),(14,35),(15,9),(15,35),(16,6),(17,12),(17,31),(18,13),(18,31),(19,16),(20,16),(21,11),(21,32),(22,11),(22,33),(23,26),(24,27),(25,21),(25,22),(25,31),(26,12),(26,21),(27,13),(27,22),(28,17),(28,18),(29,17),(29,25),(29,26),(30,18),(30,25),(30,27),(31,10),(31,32),(31,33),(32,14),(32,34),(33,15),(33,34),(34,35),(35,19),(35,20)],36)
 => ([(3,18),(3,19),(4,5),(4,19),(5,18),(6,10),(6,11),(6,18),(6,19),(6,24),(7,15),(7,16),(7,27),(7,32),(7,33),(7,34),(7,35),(8,9),(8,11),(8,18),(8,23),(8,24),(8,26),(8,29),(8,31),(8,33),(8,35),(9,10),(9,19),(9,23),(9,24),(9,25),(9,28),(9,30),(9,32),(9,34),(10,11),(10,18),(10,23),(10,26),(10,29),(10,31),(10,33),(10,35),(11,19),(11,23),(11,25),(11,28),(11,30),(11,32),(11,34),(12,23),(12,25),(12,26),(12,28),(12,29),(12,30),(12,31),(12,32),(12,33),(12,34),(12,35),(13,14),(13,16),(13,20),(13,22),(13,27),(13,28),(13,30),(13,32),(13,33),(13,34),(13,35),(14,15),(14,20),(14,21),(14,27),(14,29),(14,31),(14,32),(14,33),(14,34),(14,35),(15,16),(15,20),(15,22),(15,27),(15,28),(15,30),(15,32),(15,34),(15,35),(16,20),(16,21),(16,27),(16,29),(16,31),(16,33),(16,34),(16,35),(17,20),(17,21),(17,22),(17,27),(17,28),(17,29),(17,30),(17,31),(17,32),(17,33),(17,34),(17,35),(18,19),(18,23),(18,25),(18,28),(18,30),(18,32),(18,34),(19,23),(19,26),(19,29),(19,31),(19,33),(19,35),(20,23),(20,25),(20,26),(20,30),(20,31),(20,32),(20,33),(20,34),(20,35),(21,22),(21,23),(21,25),(21,26),(21,28),(21,30),(21,31),(21,32),(21,33),(21,34),(21,35),(22,23),(22,25),(22,26),(22,29),(22,30),(22,31),(22,32),(22,33),(22,34),(22,35),(23,24),(23,27),(23,28),(23,29),(24,25),(24,26),(24,28),(24,29),(24,30),(24,31),(24,32),(24,33),(24,34),(24,35),(25,26),(25,27),(25,28),(25,29),(25,31),(25,33),(25,35),(26,27),(26,28),(26,29),(26,30),(26,32),(26,34),(27,30),(27,31),(27,32),(27,33),(27,34),(27,35),(28,29),(28,31),(28,33),(28,35),(29,30),(29,32),(29,34),(30,31),(30,33),(30,35),(31,32),(31,34),(32,33),(32,35),(33,34),(34,35)],36)
 => ([(0,36),(1,36),(2,36),(3,18),(3,19),(3,36),(4,5),(4,19),(4,36),(5,18),(5,36),(6,10),(6,11),(6,18),(6,19),(6,24),(6,36),(7,15),(7,16),(7,27),(7,32),(7,33),(7,34),(7,35),(7,36),(8,9),(8,11),(8,18),(8,23),(8,24),(8,26),(8,29),(8,31),(8,33),(8,35),(8,36),(9,10),(9,19),(9,23),(9,24),(9,25),(9,28),(9,30),(9,32),(9,34),(9,36),(10,11),(10,18),(10,23),(10,26),(10,29),(10,31),(10,33),(10,35),(10,36),(11,19),(11,23),(11,25),(11,28),(11,30),(11,32),(11,34),(11,36),(12,23),(12,25),(12,26),(12,28),(12,29),(12,30),(12,31),(12,32),(12,33),(12,34),(12,35),(12,36),(13,14),(13,16),(13,20),(13,22),(13,27),(13,28),(13,30),(13,32),(13,33),(13,34),(13,35),(13,36),(14,15),(14,20),(14,21),(14,27),(14,29),(14,31),(14,32),(14,33),(14,34),(14,35),(14,36),(15,16),(15,20),(15,22),(15,27),(15,28),(15,30),(15,32),(15,34),(15,35),(15,36),(16,20),(16,21),(16,27),(16,29),(16,31),(16,33),(16,34),(16,35),(16,36),(17,20),(17,21),(17,22),(17,27),(17,28),(17,29),(17,30),(17,31),(17,32),(17,33),(17,34),(17,35),(17,36),(18,19),(18,23),(18,25),(18,28),(18,30),(18,32),(18,34),(18,36),(19,23),(19,26),(19,29),(19,31),(19,33),(19,35),(19,36),(20,23),(20,25),(20,26),(20,30),(20,31),(20,32),(20,33),(20,34),(20,35),(20,36),(21,22),(21,23),(21,25),(21,26),(21,28),(21,30),(21,31),(21,32),(21,33),(21,34),(21,35),(21,36),(22,23),(22,25),(22,26),(22,29),(22,30),(22,31),(22,32),(22,33),(22,34),(22,35),(22,36),(23,24),(23,27),(23,28),(23,29),(23,36),(24,25),(24,26),(24,28),(24,29),(24,30),(24,31),(24,32),(24,33),(24,34),(24,35),(24,36),(25,26),(25,27),(25,28),(25,29),(25,31),(25,33),(25,35),(25,36),(26,27),(26,28),(26,29),(26,30),(26,32),(26,34),(26,36),(27,30),(27,31),(27,32),(27,33),(27,34),(27,35),(27,36),(28,29),(28,31),(28,33),(28,35),(28,36),(29,30),(29,32),(29,34),(29,36),(30,31),(30,33),(30,35),(30,36),(31,32),(31,34),(31,36),(32,33),(32,35),(32,36),(33,34),(33,36),(34,35),(34,36),(35,36)],37)
 => ? = 166
['A',7]
 => ([(0,17),(1,16),(2,26),(2,27),(3,24),(3,26),(4,25),(4,27),(5,16),(5,24),(6,17),(6,25),(8,10),(9,11),(10,12),(11,13),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,21),(18,22),(19,10),(19,21),(20,11),(20,22),(21,12),(21,23),(22,13),(22,23),(23,14),(23,15),(24,8),(24,19),(25,9),(25,20),(26,18),(26,19),(27,18),(27,20)],28)
 => ?
 => ?
 => ? = 137
['B',7]
 => ([(0,28),(1,27),(2,28),(2,47),(3,45),(3,46),(4,46),(4,47),(5,45),(5,48),(6,27),(6,48),(8,25),(9,23),(10,24),(11,26),(12,13),(13,7),(14,21),(15,22),(16,18),(17,16),(18,20),(19,17),(20,15),(21,19),(22,13),(23,11),(23,35),(24,9),(24,34),(25,10),(25,33),(26,12),(26,22),(27,14),(28,8),(28,36),(29,30),(29,33),(30,31),(30,41),(31,34),(31,42),(32,30),(32,43),(33,24),(33,31),(34,23),(34,40),(35,15),(35,26),(36,25),(36,29),(37,29),(37,32),(38,32),(38,39),(39,19),(39,43),(40,20),(40,35),(41,16),(41,42),(42,18),(42,40),(43,17),(43,41),(44,21),(44,39),(45,38),(45,44),(46,37),(46,38),(47,36),(47,37),(48,14),(48,44)],49)
 => ?
 => ?
 => ? = 4015
['C',7]
 => ([(0,28),(1,27),(2,28),(2,47),(3,45),(3,46),(4,46),(4,47),(5,45),(5,48),(6,27),(6,48),(8,25),(9,23),(10,24),(11,26),(12,13),(13,7),(14,21),(15,22),(16,18),(17,16),(18,20),(19,17),(20,15),(21,19),(22,13),(23,11),(23,35),(24,9),(24,34),(25,10),(25,33),(26,12),(26,22),(27,14),(28,8),(28,36),(29,30),(29,33),(30,31),(30,41),(31,34),(31,42),(32,30),(32,43),(33,24),(33,31),(34,23),(34,40),(35,15),(35,26),(36,25),(36,29),(37,29),(37,32),(38,32),(38,39),(39,19),(39,43),(40,20),(40,35),(41,16),(41,42),(42,18),(42,40),(43,17),(43,41),(44,21),(44,39),(45,38),(45,44),(46,37),(46,38),(47,36),(47,37),(48,14),(48,44)],49)
 => ?
 => ?
 => ? = 4015
['D',7]
 => ([(0,34),(1,33),(2,27),(3,31),(3,37),(4,30),(4,31),(5,27),(5,30),(6,33),(6,34),(6,37),(8,26),(9,25),(10,14),(11,41),(12,41),(13,39),(14,7),(15,16),(16,14),(17,20),(17,39),(18,21),(18,39),(19,22),(20,23),(20,40),(21,24),(21,40),(22,29),(23,11),(23,38),(24,12),(24,38),(25,10),(25,16),(26,9),(26,32),(27,19),(28,22),(28,36),(29,11),(29,12),(30,19),(30,28),(31,28),(31,35),(32,15),(32,25),(33,13),(33,17),(34,13),(34,18),(35,20),(35,21),(35,36),(36,23),(36,24),(36,29),(37,17),(37,18),(37,35),(38,32),(38,41),(39,8),(39,40),(40,26),(40,38),(41,15)],42)
 => ?
 => ?
 => ? = 960
['E',7]
 => ([(0,49),(1,40),(2,41),(3,40),(3,46),(4,46),(4,52),(5,41),(5,51),(6,49),(6,51),(6,52),(7,9),(9,8),(10,48),(11,39),(12,24),(13,14),(13,47),(14,27),(15,22),(15,34),(16,23),(16,33),(17,60),(18,57),(19,56),(20,58),(21,13),(21,58),(22,11),(22,62),(23,10),(23,61),(24,7),(25,38),(26,24),(27,26),(28,17),(28,59),(29,28),(29,53),(30,42),(31,19),(31,53),(32,18),(32,60),(33,15),(33,35),(33,61),(34,21),(34,62),(35,22),(35,54),(36,37),(36,56),(37,18),(37,55),(38,12),(38,26),(39,25),(40,30),(41,45),(42,17),(42,32),(43,36),(43,44),(43,53),(44,32),(44,37),(44,59),(45,19),(45,36),(46,30),(46,50),(47,27),(47,38),(48,20),(48,21),(49,29),(49,31),(50,28),(50,42),(50,44),(51,31),(51,43),(51,45),(52,29),(52,43),(52,50),(53,16),(53,56),(53,59),(54,20),(54,62),(55,57),(55,61),(56,23),(56,55),(57,54),(58,25),(58,47),(59,33),(59,55),(59,60),(60,35),(60,57),(61,34),(61,48),(61,54),(62,39),(62,58)],63)
 => ?
 => ?
 => ? = 1096
['A',8]
 => ([(0,20),(1,19),(2,31),(2,33),(3,32),(3,33),(4,31),(4,34),(5,32),(5,35),(6,19),(6,34),(7,20),(7,35),(9,15),(10,16),(11,17),(12,18),(13,11),(14,12),(15,13),(16,14),(17,8),(18,8),(19,9),(20,10),(21,22),(21,23),(22,11),(22,24),(23,12),(23,24),(24,17),(24,18),(25,21),(25,27),(26,21),(26,28),(27,13),(27,22),(28,14),(28,23),(29,15),(29,27),(30,16),(30,28),(31,25),(31,29),(32,26),(32,30),(33,25),(33,26),(34,9),(34,29),(35,10),(35,30)],36)
 => ?
 => ?
 => ? = 249
['B',8]
 => ([(0,33),(1,32),(2,33),(2,62),(3,60),(3,61),(4,59),(4,61),(5,60),(5,62),(6,59),(6,63),(7,32),(7,63),(9,30),(10,28),(11,27),(12,29),(13,31),(14,15),(15,8),(16,25),(17,26),(18,20),(19,18),(20,22),(21,19),(22,24),(23,21),(24,17),(25,23),(26,15),(27,13),(27,46),(28,11),(28,45),(29,10),(29,43),(30,12),(30,44),(31,14),(31,26),(32,16),(33,9),(33,47),(34,35),(34,40),(35,38),(35,43),(36,34),(36,39),(37,34),(37,44),(38,41),(38,53),(39,40),(39,55),(40,38),(40,54),(41,45),(41,56),(42,39),(42,57),(43,28),(43,41),(44,29),(44,35),(45,27),(45,52),(46,17),(46,31),(47,30),(47,37),(48,36),(48,42),(49,36),(49,37),(50,42),(50,51),(51,23),(51,57),(52,24),(52,46),(53,20),(53,56),(54,18),(54,53),(55,19),(55,54),(56,22),(56,52),(57,21),(57,55),(58,25),(58,51),(59,50),(59,58),(60,48),(60,49),(61,48),(61,50),(62,47),(62,49),(63,16),(63,58)],64)
 => ?
 => ?
 => ? = 9655
['C',8]
 => ([(0,33),(1,32),(2,33),(2,62),(3,60),(3,61),(4,59),(4,61),(5,60),(5,62),(6,59),(6,63),(7,32),(7,63),(9,30),(10,28),(11,27),(12,29),(13,31),(14,15),(15,8),(16,25),(17,26),(18,20),(19,18),(20,22),(21,19),(22,24),(23,21),(24,17),(25,23),(26,15),(27,13),(27,46),(28,11),(28,45),(29,10),(29,43),(30,12),(30,44),(31,14),(31,26),(32,16),(33,9),(33,47),(34,35),(34,40),(35,38),(35,43),(36,34),(36,39),(37,34),(37,44),(38,41),(38,53),(39,40),(39,55),(40,38),(40,54),(41,45),(41,56),(42,39),(42,57),(43,28),(43,41),(44,29),(44,35),(45,27),(45,52),(46,17),(46,31),(47,30),(47,37),(48,36),(48,42),(49,36),(49,37),(50,42),(50,51),(51,23),(51,57),(52,24),(52,46),(53,20),(53,56),(54,18),(54,53),(55,19),(55,54),(56,22),(56,52),(57,21),(57,55),(58,25),(58,51),(59,50),(59,58),(60,48),(60,49),(61,48),(61,50),(62,47),(62,49),(63,16),(63,58)],64)
 => ?
 => ?
 => ? = 9655
['D',8]
 => ([(0,41),(1,40),(2,34),(3,45),(3,46),(4,45),(4,50),(5,44),(5,46),(6,34),(6,44),(7,40),(7,41),(7,50),(9,33),(10,31),(11,32),(12,16),(13,53),(14,54),(15,54),(16,8),(17,16),(18,22),(18,53),(19,23),(19,53),(20,24),(21,25),(22,29),(22,55),(23,30),(23,55),(24,26),(25,17),(26,39),(27,14),(27,52),(28,15),(28,52),(29,27),(29,51),(30,28),(30,51),(31,11),(31,42),(32,9),(32,36),(33,12),(33,17),(34,20),(35,38),(35,49),(36,25),(36,33),(37,24),(37,38),(38,26),(38,47),(39,14),(39,15),(40,13),(40,18),(41,13),(41,19),(42,32),(42,43),(43,21),(43,36),(44,20),(44,37),(45,35),(45,48),(46,35),(46,37),(47,27),(47,28),(47,39),(48,22),(48,23),(48,49),(49,29),(49,30),(49,47),(50,18),(50,19),(50,48),(51,42),(51,52),(52,43),(52,54),(53,10),(53,55),(54,21),(55,31),(55,51)],56)
 => ?
 => ?
 => ? = 2684
['E',8]
 => ([(0,86),(1,74),(2,75),(3,93),(3,98),(4,92),(4,93),(5,74),(5,97),(6,75),(6,92),(7,86),(7,97),(7,98),(8,12),(10,11),(11,9),(12,10),(13,73),(14,91),(15,24),(15,90),(16,71),(17,70),(18,40),(19,21),(19,72),(20,23),(20,96),(21,46),(22,52),(23,84),(24,22),(24,79),(25,57),(25,66),(26,36),(26,65),(27,39),(27,68),(28,38),(28,67),(29,118),(30,100),(31,104),(32,105),(33,111),(34,113),(35,20),(35,115),(36,15),(36,101),(37,16),(37,111),(38,17),(38,112),(39,14),(39,110),(40,8),(41,55),(41,107),(42,58),(42,102),(43,34),(43,108),(44,72),(45,38),(45,106),(46,40),(47,53),(48,36),(48,104),(49,50),(50,44),(51,41),(51,100),(52,49),(53,76),(54,30),(54,102),(55,32),(55,99),(56,26),(56,48),(56,116),(57,28),(57,45),(57,114),(58,43),(58,109),(59,32),(59,113),(60,56),(60,119),(61,88),(62,45),(62,103),(63,29),(63,115),(64,31),(64,116),(65,37),(65,101),(66,35),(66,114),(67,60),(67,112),(68,25),(68,77),(68,110),(69,13),(69,83),(70,61),(71,69),(72,18),(72,46),(73,19),(73,44),(74,85),(75,47),(76,34),(76,59),(77,57),(77,62),(77,117),(78,55),(78,59),(78,108),(79,52),(79,82),(80,51),(80,87),(80,102),(81,53),(81,95),(82,49),(82,83),(83,50),(83,73),(84,31),(84,48),(85,30),(85,51),(86,42),(86,54),(87,41),(87,78),(87,109),(88,33),(88,37),(89,69),(89,82),(90,79),(90,89),(91,35),(91,63),(92,47),(92,81),(93,81),(93,94),(94,58),(94,87),(94,95),(95,43),(95,76),(95,78),(96,56),(96,64),(96,84),(97,54),(97,80),(97,85),(98,42),(98,80),(98,94),(99,105),(99,117),(100,39),(100,107),(101,90),(101,111),(102,27),(102,100),(102,109),(103,29),(103,106),(104,33),(104,101),(105,103),(106,112),(106,118),(107,99),(107,110),(108,77),(108,99),(108,113),(109,68),(109,107),(109,108),(110,66),(110,91),(110,117),(111,71),(111,89),(112,70),(112,119),(113,62),(113,105),(114,67),(114,106),(114,115),(115,60),(115,96),(115,118),(116,65),(116,88),(116,104),(117,63),(117,103),(117,114),(118,64),(118,119),(119,61),(119,116)],120)
 => ?
 => ?
 => ? = 3200
Description
The number of connected components of the friends and strangers graph. Let $X$ and $Y$ be graphs with the same vertex set $\{1,\dots,n\}$. Then the friends-and-strangers graph has as vertex set the set of permutations $\mathfrak S_n$ and edges $\left(\sigma, (i, j)\circ\sigma\right)$ if $(i, j)$ is an edge of $X$ and $\left(\sigma(i), \sigma(j)\right)$ is an edge of $Y$. This statistic is the number of connected components of the friends and strangers graphs where $X=Y$. For example, if $X$ is a complete graph the statistic is $1$, if $X$ has no edges, the statistic is $n!$, and if $X$ is the path graph, the statistic is $$ \sum_{k=0}^{\lfloor n/2\rfloor} (-1)^k (n-k)!\binom{n-k}{k}, $$ see [thm. 2.2, 3].