Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000737
(load all 2 compositions to match this statistic)
Mapping
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
St000737: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [[1]]
 => [[1]]
 => 1
[[1,2]]
 => [[2,0],[1]]
 => [[1,2]]
 => 1
[[1],[2]]
 => [[1,1],[1]]
 => [[1],[2]]
 => 1
[[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => 1
[[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => 1
[[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => 1
[[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => 1
[[1,2,3,4]]
 => [[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4]]
 => 1
[[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4],[2]]
 => 1
[[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4],[3]]
 => 1
[[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3],[4]]
 => 1
[[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2,4]]
 => 4
[[1,2],[3,4]]
 => [[2,2,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3,4]]
 => 4
[[1,4],[2],[3]]
 => [[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4],[2],[3]]
 => 1
[[1,3],[2],[4]]
 => [[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2],[4]]
 => 1
[[1,2],[3],[4]]
 => [[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3],[4]]
 => 1
[[1],[2],[3],[4]]
 => [[1,1,1,1],[1,1,1],[1,1],[1]]
 => [[1],[2],[3],[4]]
 => 1
[[1,2,3,4,5]]
 => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,5]]
 => 1
[[1,3,4,5],[2]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4,5],[2]]
 => 1
[[1,2,4,5],[3]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4,5],[3]]
 => 1
[[1,2,3,5],[4]]
 => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,5],[4]]
 => 1
[[1,2,3,4],[5]]
 => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4],[5]]
 => 1
[[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,5],[2,4]]
 => 4
[[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,5],[3,4]]
 => 4
[[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4],[2,5]]
 => 5
[[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4],[3,5]]
 => 5
[[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3],[4,5]]
 => 5
[[1,4,5],[2],[3]]
 => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4,5],[2],[3]]
 => 1
[[1,3,5],[2],[4]]
 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3,5],[2],[4]]
 => 1
[[1,2,5],[3],[4]]
 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2,5],[3],[4]]
 => 1
[[1,3,4],[2],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4],[2],[5]]
 => 1
[[1,2,4],[3],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4],[3],[5]]
 => 1
[[1,2,3],[4],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3],[4],[5]]
 => 1
[[1,4],[2,5],[3]]
 => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4],[2,5],[3]]
 => 5
[[1,3],[2,5],[4]]
 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2,5],[4]]
 => 5
[[1,2],[3,5],[4]]
 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3,5],[4]]
 => 5
[[1,3],[2,4],[5]]
 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2,4],[5]]
 => 4
[[1,2],[3,4],[5]]
 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3,4],[5]]
 => 4
[[1,5],[2],[3],[4]]
 => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
 => [[1,5],[2],[3],[4]]
 => 1
[[1,4],[2],[3],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4],[2],[3],[5]]
 => 1
[[1,3],[2],[4],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2],[4],[5]]
 => 1
[[1,2],[3],[4],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3],[4],[5]]
 => 1
[[1],[2],[3],[4],[5]]
 => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
 => [[1],[2],[3],[4],[5]]
 => 1
[[1,2,3,4,5,6]]
 => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,5,6]]
 => 1
[[1,3,4,5,6],[2]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4,5,6],[2]]
 => 1
[[1,2,4,5,6],[3]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4,5,6],[3]]
 => 1
[[1,2,3,5,6],[4]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,5,6],[4]]
 => 1
[[1,2,3,4,6],[5]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,6],[5]]
 => 1
[[1,2,3,4,5],[6]]
 => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,5],[6]]
 => 1
[[1,3,5,6],[2,4]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,5,6],[2,4]]
 => 4
Description
The last entry on the main diagonal of a semistandard tableau.
Matching statistic: St000735
(load all 2 compositions to match this statistic)
Mapping
St000735: Standard tableaux ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => ? = 1
[[1,2]]
 => 1
[[1],[2]]
 => 1
[[1,2,3]]
 => 1
[[1,3],[2]]
 => 1
[[1,2],[3]]
 => 1
[[1],[2],[3]]
 => 1
[[1,2,3,4]]
 => 1
[[1,3,4],[2]]
 => 1
[[1,2,4],[3]]
 => 1
[[1,2,3],[4]]
 => 1
[[1,3],[2,4]]
 => 4
[[1,2],[3,4]]
 => 4
[[1,4],[2],[3]]
 => 1
[[1,3],[2],[4]]
 => 1
[[1,2],[3],[4]]
 => 1
[[1],[2],[3],[4]]
 => 1
[[1,2,3,4,5]]
 => 1
[[1,3,4,5],[2]]
 => 1
[[1,2,4,5],[3]]
 => 1
[[1,2,3,5],[4]]
 => 1
[[1,2,3,4],[5]]
 => 1
[[1,3,5],[2,4]]
 => 4
[[1,2,5],[3,4]]
 => 4
[[1,3,4],[2,5]]
 => 5
[[1,2,4],[3,5]]
 => 5
[[1,2,3],[4,5]]
 => 5
[[1,4,5],[2],[3]]
 => 1
[[1,3,5],[2],[4]]
 => 1
[[1,2,5],[3],[4]]
 => 1
[[1,3,4],[2],[5]]
 => 1
[[1,2,4],[3],[5]]
 => 1
[[1,2,3],[4],[5]]
 => 1
[[1,4],[2,5],[3]]
 => 5
[[1,3],[2,5],[4]]
 => 5
[[1,2],[3,5],[4]]
 => 5
[[1,3],[2,4],[5]]
 => 4
[[1,2],[3,4],[5]]
 => 4
[[1,5],[2],[3],[4]]
 => 1
[[1,4],[2],[3],[5]]
 => 1
[[1,3],[2],[4],[5]]
 => 1
[[1,2],[3],[4],[5]]
 => 1
[[1],[2],[3],[4],[5]]
 => 1
[[1,2,3,4,5,6]]
 => 1
[[1,3,4,5,6],[2]]
 => 1
[[1,2,4,5,6],[3]]
 => 1
[[1,2,3,5,6],[4]]
 => 1
[[1,2,3,4,6],[5]]
 => 1
[[1,2,3,4,5],[6]]
 => 1
[[1,3,5,6],[2,4]]
 => 4
[[1,2,5,6],[3,4]]
 => 4
Description
The last entry on the main diagonal of a standard tableau.
Matching statistic: St000181
(load all 8 compositions to match this statistic)
Mapping
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St000181: Posets ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 25%
Values
[[1]]
 => [[1]]
 => [[1]]
 => ([],1)
 => 1
[[1,2]]
 => [[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => 1
[[1],[2]]
 => [[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => 1
[[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => ([(0,2),(2,1)],3)
 => 1
[[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => ([],1)
 => 1
[[1,2,3,4]]
 => [[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4]]
 => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14)
 => ? = 1
[[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4],[2]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ? = 1
[[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4],[3]]
 => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
 => ? = 1
[[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3],[4]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ? = 1
[[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2,4]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ? = 4
[[1,2],[3,4]]
 => [[2,2,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3,4]]
 => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8)
 => ? = 4
[[1,4],[2],[3]]
 => [[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4],[2],[3]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[1,3],[2],[4]]
 => [[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2],[4]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,2],[3],[4]]
 => [[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3],[4]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[1],[2],[3],[4]]
 => [[1,1,1,1],[1,1,1],[1,1],[1]]
 => [[1],[2],[3],[4]]
 => ([],1)
 => 1
[[1,2,3,4,5]]
 => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,5]]
 => ([(0,1),(1,2),(1,3),(2,7),(2,23),(3,6),(3,23),(4,27),(5,28),(6,4),(6,29),(7,5),(7,30),(8,15),(8,25),(9,16),(9,26),(10,21),(10,22),(11,35),(11,36),(12,35),(12,37),(13,36),(13,38),(14,34),(15,32),(16,33),(17,14),(17,39),(18,14),(18,40),(19,15),(19,39),(20,16),(20,40),(21,8),(21,19),(21,31),(22,9),(22,20),(22,31),(23,10),(23,29),(23,30),(24,17),(24,18),(24,31),(25,11),(25,13),(25,32),(26,11),(26,12),(26,33),(27,17),(27,19),(28,18),(28,20),(29,21),(29,24),(29,27),(30,22),(30,24),(30,28),(31,25),(31,26),(31,39),(31,40),(32,35),(32,38),(33,36),(33,37),(34,37),(34,38),(35,41),(36,41),(37,41),(38,41),(39,12),(39,32),(39,34),(40,13),(40,33),(40,34)],42)
 => ? = 1
[[1,3,4,5],[2]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4,5],[2]]
 => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28)
 => ? = 1
[[1,2,4,5],[3]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4,5],[3]]
 => ([(0,2),(0,3),(1,5),(2,1),(3,4),(3,7),(4,24),(5,8),(5,32),(6,13),(6,31),(7,11),(7,12),(7,24),(8,26),(9,16),(9,23),(10,19),(10,20),(11,29),(11,32),(12,10),(12,28),(12,29),(13,17),(13,30),(14,35),(15,34),(15,35),(16,34),(17,33),(18,36),(19,21),(20,27),(21,14),(22,14),(22,33),(23,18),(23,34),(24,6),(24,28),(25,21),(25,22),(26,17),(26,22),(27,15),(27,16),(28,20),(28,31),(29,19),(29,25),(30,15),(30,23),(30,33),(31,9),(31,27),(31,30),(32,25),(32,26),(33,18),(33,35),(34,36),(35,36)],37)
 => ? = 1
[[1,2,3,5],[4]]
 => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,5],[4]]
 => ([(0,2),(0,3),(1,7),(1,10),(2,1),(3,4),(3,6),(4,25),(5,24),(6,13),(6,25),(7,8),(7,31),(8,28),(9,20),(9,21),(10,29),(10,31),(11,16),(11,30),(12,17),(12,23),(13,9),(13,26),(13,29),(14,35),(15,33),(15,35),(16,34),(17,33),(18,36),(19,17),(20,27),(21,19),(22,14),(22,34),(23,18),(23,33),(24,12),(24,19),(25,5),(25,26),(26,21),(26,24),(27,14),(27,15),(28,16),(28,22),(29,20),(29,32),(30,15),(30,23),(30,34),(31,11),(31,28),(31,32),(32,22),(32,27),(32,30),(33,36),(34,18),(34,35),(35,36)],37)
 => ? = 1
[[1,2,3,4],[5]]
 => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4],[5]]
 => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28)
 => ? = 1
[[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,5],[2,4]]
 => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
 => ? = 4
[[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,5],[3,4]]
 => ([(0,3),(0,4),(1,6),(2,7),(2,10),(3,1),(4,2),(5,20),(6,19),(7,5),(7,21),(8,14),(8,17),(9,12),(9,18),(10,9),(10,19),(10,21),(11,24),(12,25),(13,23),(14,22),(15,22),(15,23),(16,13),(16,25),(17,11),(17,22),(18,15),(18,17),(18,25),(19,12),(19,16),(20,13),(20,14),(20,15),(21,8),(21,16),(21,18),(21,20),(22,24),(23,24),(25,11),(25,23)],26)
 => ? = 4
[[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4],[2,5]]
 => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19)
 => ? = 5
[[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4],[3,5]]
 => ([(0,1),(1,6),(1,7),(1,8),(2,22),(3,17),(4,5),(4,16),(5,12),(5,18),(6,20),(6,23),(7,19),(7,20),(8,9),(8,19),(8,23),(9,13),(9,14),(10,24),(12,24),(13,15),(14,16),(15,10),(16,3),(16,18),(17,11),(18,17),(18,24),(19,4),(19,14),(20,2),(20,21),(21,15),(21,22),(22,10),(22,12),(23,13),(23,21),(24,11)],25)
 => ? = 5
[[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3],[4,5]]
 => ([(0,2),(1,9),(2,6),(2,7),(2,8),(3,23),(4,19),(5,13),(5,20),(6,18),(6,21),(7,15),(7,18),(8,4),(8,15),(8,21),(9,14),(9,17),(10,26),(11,25),(12,24),(12,25),(13,27),(14,24),(15,1),(16,11),(16,27),(17,10),(17,24),(18,3),(18,22),(19,13),(19,16),(20,12),(20,17),(20,27),(21,5),(21,19),(21,22),(22,16),(22,20),(22,23),(23,11),(23,12),(23,14),(24,26),(25,26),(27,10),(27,25)],28)
 => ? = 5
[[1,4,5],[2],[3]]
 => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4,5],[2],[3]]
 => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14)
 => ? = 1
[[1,3,5],[2],[4]]
 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3,5],[2],[4]]
 => ([(0,5),(0,6),(1,13),(2,17),(3,4),(3,18),(4,8),(4,9),(4,19),(5,16),(6,3),(6,7),(6,16),(7,14),(7,18),(8,11),(8,15),(9,10),(9,11),(10,20),(11,20),(13,2),(14,13),(15,17),(15,20),(16,1),(16,14),(17,12),(18,19),(19,10),(19,15),(20,12)],21)
 => ? = 1
[[1,2,5],[3],[4]]
 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2,5],[3],[4]]
 => ([(0,9),(0,10),(1,14),(2,13),(3,12),(3,14),(4,12),(4,13),(5,8),(6,3),(7,11),(8,1),(9,5),(9,18),(10,7),(10,18),(11,2),(11,4),(12,15),(12,16),(13,15),(14,16),(15,17),(16,17),(18,6)],19)
 => ? = 1
[[1,3,4],[2],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4],[2],[5]]
 => ([(0,5),(0,6),(1,16),(2,15),(3,12),(4,13),(5,2),(5,14),(6,1),(6,14),(7,10),(7,11),(9,17),(10,3),(10,17),(11,4),(11,17),(12,8),(13,8),(14,7),(14,15),(14,16),(15,9),(15,10),(16,9),(16,11),(17,12),(17,13)],18)
 => ? = 1
[[1,2,4],[3],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4],[3],[5]]
 => ([(0,5),(0,6),(1,17),(2,9),(2,19),(3,4),(3,18),(4,8),(4,13),(5,16),(6,3),(6,7),(6,16),(7,14),(7,18),(8,10),(8,11),(9,11),(9,15),(10,20),(11,20),(13,10),(14,19),(15,17),(15,20),(16,2),(16,14),(17,12),(18,13),(19,1),(19,15),(20,12)],21)
 => ? = 1
[[1,2,3],[4],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3],[4],[5]]
 => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14)
 => ? = 1
[[1,4],[2,5],[3]]
 => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4],[2,5],[3]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ? = 5
[[1,3],[2,5],[4]]
 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2,5],[4]]
 => ([(0,6),(1,12),(2,10),(3,7),(3,8),(4,7),(4,9),(5,3),(5,4),(5,12),(6,1),(6,5),(7,13),(8,13),(9,10),(9,13),(10,11),(12,2),(12,8),(12,9),(13,11)],14)
 => ? = 5
[[1,2],[3,5],[4]]
 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3,5],[4]]
 => ([(0,5),(0,6),(1,10),(2,9),(3,9),(3,11),(4,10),(4,11),(5,7),(6,8),(7,2),(7,3),(8,1),(8,4),(9,12),(10,13),(11,12),(11,13),(12,14),(13,14)],15)
 => ? = 5
[[1,3],[2,4],[5]]
 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2,4],[5]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ? = 4
[[1,2],[3,4],[5]]
 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3,4],[5]]
 => ([(0,6),(1,12),(2,10),(3,7),(3,8),(4,7),(4,9),(5,3),(5,4),(5,12),(6,1),(6,5),(7,13),(8,13),(9,10),(9,13),(10,11),(12,2),(12,8),(12,9),(13,11)],14)
 => ? = 4
[[1,5],[2],[3],[4]]
 => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
 => [[1,5],[2],[3],[4]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[1,4],[2],[3],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4],[2],[3],[5]]
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 1
[[1,3],[2],[4],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2],[4],[5]]
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 1
[[1,2],[3],[4],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3],[4],[5]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[1],[2],[3],[4],[5]]
 => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
 => [[1],[2],[3],[4],[5]]
 => ([],1)
 => 1
[[1,2,3,4,5,6]]
 => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,5,6]]
 => ([(0,1),(1,2),(1,3),(2,9),(2,53),(3,8),(3,53),(4,60),(5,61),(6,4),(6,64),(7,5),(7,65),(8,6),(8,62),(9,7),(9,63),(10,35),(10,36),(11,54),(11,55),(12,37),(12,56),(13,38),(13,57),(14,17),(14,58),(15,18),(15,59),(16,11),(16,110),(16,111),(17,87),(18,88),(19,90),(20,79),(20,102),(21,80),(21,103),(22,77),(22,83),(23,78),(23,84),(24,79),(24,85),(25,80),(25,86),(26,81),(26,94),(27,82),(27,95),(28,75),(28,76),(28,93),(29,22),(29,110),(29,115),(30,23),(30,111),(30,114),(31,43),(31,73),(32,44),(32,74),(33,45),(33,73),(34,46),(34,74),(35,12),(35,47),(35,66),(36,13),(36,48),(36,66),(37,14),(37,45),(37,69),(38,15),(38,46),(38,70),(39,27),(39,67),(39,98),(40,26),(40,68),(40,99),(41,20),(41,67),(41,91),(42,21),(42,68),(42,92),(43,19),(43,104),(44,19),(44,105),(45,17),(45,96),(46,18),(46,97),(47,33),(47,37),(47,112),(48,34),(48,38),(48,113),(49,50),(49,51),(49,66),(50,31),(50,52),(50,112),(51,32),(51,52),(51,113),(52,43),(52,44),(52,72),(53,10),(53,62),(53,63),(54,20),(54,24),(54,71),(55,21),(55,25),(55,71),(56,16),(56,30),(56,69),(57,16),(57,29),(57,70),(58,39),(58,41),(58,87),(59,40),(59,42),(59,88),(60,31),(60,33),(61,32),(61,34),(62,35),(62,49),(62,64),(63,36),(63,49),(63,65),(64,47),(64,50),(64,60),(65,48),(65,51),(65,61),(66,56),(66,57),(66,112),(66,113),(67,28),(67,82),(67,102),(67,129),(68,28),(68,81),(68,103),(68,130),(69,58),(69,96),(69,110),(69,114),(70,59),(70,97),(70,111),(70,115),(71,85),(71,86),(71,102),(71,103),(72,104),(72,105),(72,114),(72,115),(73,22),(73,96),(73,104),(74,23),(74,97),(74,105),(75,117),(75,125),(76,117),(76,126),(77,26),(77,108),(77,121),(78,27),(78,109),(78,122),(79,123),(80,124),(81,75),(81,106),(81,119),(82,76),(82,107),(82,120),(83,24),(83,91),(83,121),(84,25),(84,92),(84,122),(85,89),(85,106),(85,123),(86,89),(86,107),(86,124),(87,91),(87,98),(88,92),(88,99),(89,127),(89,128),(90,108),(90,109),(91,79),(91,129),(92,80),(92,130),(93,125),(93,126),(94,119),(95,120),(96,83),(96,87),(96,100),(97,84),(97,88),(97,101),(98,95),(98,129),(99,94),(99,130),(100,98),(100,109),(100,121),(101,99),(101,108),(101,122),(102,93),(102,107),(102,123),(103,93),(103,106),(103,124),(104,77),(104,90),(104,100),(105,78),(105,90),(105,101),(106,125),(106,127),(107,126),(107,128),(108,94),(108,118),(109,95),(109,118),(110,41),(110,54),(110,83),(110,116),(111,42),(111,55),(111,84),(111,116),(112,29),(112,69),(112,72),(112,73),(113,30),(113,70),(113,72),(113,74),(114,39),(114,78),(114,100),(114,116),(115,40),(115,77),(115,101),(115,116),(116,67),(116,68),(116,71),(116,121),(116,122),(117,131),(118,89),(118,119),(118,120),(119,117),(119,127),(120,117),(120,128),(121,81),(121,85),(121,118),(121,129),(122,82),(122,86),(122,118),(122,130),(123,125),(123,128),(124,126),(124,127),(125,131),(126,131),(127,131),(128,131),(129,75),(129,120),(129,123),(130,76),(130,119),(130,124)],132)
 => ? = 1
[[1,3,4,5,6],[2]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4,5,6],[2]]
 => ([(0,1),(1,3),(1,4),(2,46),(3,8),(3,44),(4,9),(4,44),(5,51),(6,50),(7,6),(7,54),(8,7),(8,52),(9,5),(9,53),(10,37),(10,47),(11,34),(11,45),(12,35),(12,36),(13,20),(13,48),(14,19),(14,49),(15,77),(16,74),(17,11),(17,82),(17,84),(18,63),(18,71),(19,62),(20,2),(20,67),(21,57),(21,73),(22,75),(22,84),(23,69),(24,63),(24,65),(25,61),(25,64),(26,66),(26,72),(27,18),(27,57),(27,76),(28,19),(28,78),(29,23),(29,60),(30,25),(30,82),(30,83),(31,28),(31,55),(32,16),(32,60),(33,15),(33,55),(34,16),(34,59),(35,13),(35,38),(35,58),(36,10),(36,41),(36,58),(37,14),(37,28),(37,56),(38,20),(38,70),(39,40),(39,70),(40,15),(40,68),(41,31),(41,37),(41,81),(42,39),(42,43),(42,58),(43,33),(43,40),(43,81),(44,12),(44,52),(44,53),(45,18),(45,24),(45,59),(46,29),(46,32),(47,17),(47,22),(47,56),(48,17),(48,30),(48,67),(49,21),(49,27),(49,62),(50,31),(50,33),(51,38),(51,39),(52,36),(52,42),(52,54),(53,35),(53,42),(53,51),(54,41),(54,43),(54,50),(55,25),(55,77),(55,78),(56,49),(56,75),(56,78),(56,82),(57,26),(57,71),(57,86),(58,47),(58,48),(58,70),(58,81),(59,65),(59,71),(59,74),(60,26),(60,69),(60,74),(61,24),(61,76),(61,89),(62,73),(62,76),(63,88),(64,23),(64,89),(65,80),(65,88),(66,87),(67,46),(67,83),(67,84),(68,75),(68,77),(68,83),(69,66),(69,80),(70,22),(70,67),(70,68),(71,72),(71,88),(72,87),(73,86),(74,72),(74,80),(75,21),(75,79),(75,85),(76,63),(76,86),(77,64),(77,79),(78,61),(78,62),(78,79),(79,73),(79,89),(80,87),(81,30),(81,55),(81,56),(81,68),(82,27),(82,45),(82,61),(82,85),(83,29),(83,64),(83,85),(84,32),(84,34),(84,85),(85,57),(85,59),(85,60),(85,89),(86,66),(86,88),(88,87),(89,65),(89,69),(89,86)],90)
 => ? = 1
[[1,2,4,5,6],[3]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4,5,6],[3]]
 => ([(0,2),(0,3),(1,5),(2,8),(2,10),(3,1),(4,66),(5,6),(5,72),(6,7),(6,78),(7,57),(8,4),(8,69),(9,14),(9,76),(10,11),(10,12),(10,69),(11,72),(11,74),(12,18),(12,74),(12,79),(13,56),(13,73),(14,32),(14,70),(15,17),(15,33),(15,71),(16,39),(16,64),(17,38),(17,60),(18,16),(18,58),(18,75),(19,46),(19,49),(19,50),(20,24),(20,47),(20,48),(21,117),(22,86),(22,97),(23,89),(23,90),(24,91),(24,92),(25,103),(26,99),(26,110),(27,87),(27,88),(28,93),(29,80),(29,98),(30,80),(30,90),(30,100),(31,89),(31,107),(32,96),(33,9),(33,115),(34,24),(34,84),(34,86),(35,27),(35,118),(36,44),(36,115),(37,56),(37,87),(37,94),(38,42),(38,116),(39,40),(40,41),(41,25),(41,97),(42,32),(42,83),(43,54),(43,83),(44,21),(44,81),(45,22),(45,82),(45,114),(46,55),(46,113),(47,52),(47,92),(48,68),(48,91),(49,35),(49,114),(50,20),(50,34),(50,113),(50,114),(51,26),(51,109),(52,29),(52,105),(53,26),(53,94),(53,104),(54,25),(54,108),(55,13),(55,37),(55,85),(56,28),(56,95),(57,42),(57,43),(58,39),(58,62),(59,61),(59,62),(60,45),(60,49),(60,116),(61,43),(61,63),(61,116),(62,40),(62,63),(63,41),(63,54),(63,82),(64,21),(64,65),(65,22),(65,34),(65,117),(66,33),(66,36),(67,51),(67,53),(67,85),(68,23),(68,30),(68,106),(69,15),(69,66),(69,79),(70,37),(70,53),(70,96),(71,19),(71,60),(71,77),(71,115),(72,59),(72,78),(73,23),(73,31),(73,95),(74,58),(74,59),(75,44),(75,64),(75,77),(76,55),(76,67),(76,70),(77,45),(77,50),(77,65),(77,81),(78,38),(78,57),(78,61),(79,36),(79,71),(79,75),(80,111),(80,123),(81,67),(81,113),(81,117),(82,97),(82,108),(82,118),(83,27),(83,96),(83,108),(84,91),(84,109),(85,68),(85,73),(85,94),(85,109),(86,92),(86,102),(87,28),(87,119),(88,29),(88,112),(88,119),(89,121),(90,111),(90,121),(91,106),(92,105),(93,101),(93,111),(94,30),(94,95),(94,110),(94,119),(95,90),(95,93),(95,107),(96,87),(96,104),(97,102),(97,103),(98,123),(99,122),(100,121),(100,123),(101,120),(102,105),(102,112),(103,99),(103,112),(104,99),(104,119),(105,98),(106,89),(106,100),(107,101),(107,121),(108,88),(108,103),(108,104),(109,31),(109,106),(109,110),(110,100),(110,107),(110,122),(111,120),(112,98),(112,122),(113,48),(113,84),(113,85),(114,47),(114,86),(114,118),(115,46),(115,76),(115,81),(116,35),(116,82),(116,83),(117,51),(117,84),(118,52),(118,88),(118,102),(119,80),(119,93),(119,122),(121,120),(122,101),(122,123),(123,120)],124)
 => ? = 1
[[1,2,3,5,6],[4]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,5,6],[4]]
 => ([(0,1),(0,2),(1,5),(1,7),(2,4),(2,8),(3,54),(4,45),(5,44),(6,13),(6,71),(7,11),(7,44),(8,12),(8,18),(8,45),(9,76),(9,77),(10,58),(10,59),(11,22),(11,75),(11,80),(12,80),(12,81),(13,57),(13,72),(14,56),(14,73),(15,55),(15,60),(16,37),(16,79),(17,36),(17,78),(18,20),(18,74),(18,81),(19,41),(19,65),(20,21),(20,63),(20,85),(21,40),(21,62),(22,19),(22,61),(22,83),(23,109),(23,110),(24,87),(25,125),(26,98),(26,115),(27,96),(27,106),(28,95),(28,107),(29,98),(29,100),(30,97),(30,99),(31,114),(31,121),(32,113),(32,120),(33,93),(34,97),(34,118),(35,101),(35,102),(36,104),(37,103),(38,33),(38,127),(39,49),(40,67),(41,39),(42,46),(42,87),(43,27),(43,88),(43,90),(44,3),(44,75),(45,6),(45,74),(46,23),(46,95),(46,119),(47,32),(47,100),(47,117),(48,31),(48,99),(48,116),(49,37),(49,106),(50,36),(50,107),(51,26),(51,94),(52,28),(52,89),(52,108),(53,23),(53,96),(53,105),(54,15),(54,66),(55,38),(55,90),(56,24),(56,126),(57,25),(57,91),(58,17),(58,50),(58,89),(59,9),(59,70),(59,89),(60,16),(60,49),(60,90),(61,41),(61,66),(62,24),(62,42),(63,40),(63,86),(64,42),(64,69),(64,126),(65,25),(65,68),(66,39),(66,60),(67,28),(67,50),(68,27),(68,53),(68,125),(69,46),(69,53),(69,88),(69,108),(70,51),(70,76),(70,128),(71,10),(71,72),(71,86),(72,52),(72,59),(72,91),(73,43),(73,55),(73,126),(74,63),(74,71),(75,54),(75,61),(76,26),(76,29),(76,92),(77,30),(77,34),(77,92),(78,30),(78,48),(78,104),(79,29),(79,47),(79,103),(80,83),(80,84),(81,14),(81,84),(81,85),(82,43),(82,68),(82,69),(82,91),(83,57),(83,65),(83,82),(84,64),(84,73),(84,82),(85,56),(85,62),(85,64),(86,52),(86,58),(86,67),(87,33),(87,119),(88,96),(88,119),(88,127),(89,77),(89,78),(89,107),(89,128),(90,79),(90,106),(90,127),(91,70),(91,108),(91,125),(92,99),(92,100),(92,115),(92,118),(93,32),(93,124),(94,31),(94,115),(94,123),(95,110),(95,112),(96,109),(96,111),(97,133),(98,132),(99,35),(99,121),(99,133),(100,35),(100,120),(100,132),(101,131),(102,131),(103,98),(103,117),(104,97),(104,116),(105,94),(105,110),(106,103),(106,111),(107,34),(107,104),(107,112),(108,95),(108,105),(108,128),(109,124),(110,123),(111,117),(111,124),(112,116),(112,118),(112,123),(113,130),(114,129),(115,121),(115,122),(115,132),(116,114),(116,133),(117,113),(117,132),(118,120),(118,122),(118,133),(119,93),(119,109),(120,102),(120,130),(121,101),(121,129),(122,129),(122,130),(123,114),(123,122),(124,113),(125,51),(125,105),(126,38),(126,87),(126,88),(127,47),(127,93),(127,111),(128,48),(128,92),(128,94),(128,112),(129,131),(130,131),(132,101),(132,130),(133,102),(133,129)],134)
 => ? = 1
[[1,2,3,4,6],[5]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,6],[5]]
 => ([(0,2),(0,3),(1,6),(1,16),(2,9),(2,10),(3,1),(4,65),(5,66),(6,7),(6,73),(7,8),(7,76),(8,60),(9,4),(9,69),(10,13),(10,69),(11,35),(11,72),(12,56),(12,71),(13,18),(13,74),(13,79),(14,57),(14,70),(15,34),(15,55),(16,73),(16,74),(17,40),(17,63),(18,17),(18,59),(18,77),(19,25),(19,52),(19,53),(20,44),(20,45),(20,46),(21,101),(22,85),(23,80),(23,83),(24,90),(24,91),(25,86),(25,87),(26,100),(26,102),(27,81),(27,106),(28,92),(29,90),(29,104),(30,89),(31,93),(31,105),(32,81),(32,91),(32,107),(33,12),(33,118),(34,5),(34,115),(35,94),(36,24),(36,109),(37,39),(37,115),(38,23),(38,114),(38,117),(39,22),(39,116),(40,58),(41,21),(41,80),(42,47),(42,85),(43,28),(43,118),(44,67),(44,114),(45,33),(45,113),(46,19),(46,47),(46,113),(46,114),(47,25),(47,83),(47,97),(48,26),(48,95),(48,99),(49,21),(49,88),(50,35),(50,98),(51,49),(51,98),(52,36),(52,87),(53,68),(53,86),(54,56),(54,93),(54,95),(55,20),(55,62),(55,115),(56,30),(56,96),(57,11),(57,50),(57,84),(58,23),(58,41),(59,40),(59,78),(60,50),(60,51),(61,51),(61,64),(61,84),(62,42),(62,46),(62,116),(63,22),(63,42),(64,41),(64,49),(64,117),(65,34),(65,37),(66,33),(66,43),(67,31),(67,54),(67,82),(68,27),(68,32),(68,103),(69,15),(69,65),(69,79),(70,38),(70,44),(70,84),(71,24),(71,29),(71,96),(72,48),(72,54),(72,94),(73,14),(73,75),(73,76),(74,59),(74,75),(75,61),(75,70),(75,78),(76,57),(76,60),(76,61),(77,39),(77,62),(77,63),(78,38),(78,58),(78,64),(79,37),(79,55),(79,77),(80,26),(80,101),(80,111),(81,112),(81,121),(82,68),(82,95),(82,105),(82,111),(83,86),(83,111),(84,67),(84,72),(84,98),(84,117),(85,28),(85,97),(86,103),(87,109),(88,99),(88,101),(88,105),(89,108),(89,112),(90,122),(91,112),(91,122),(92,29),(92,109),(93,30),(93,123),(94,93),(94,99),(95,32),(95,96),(95,100),(95,123),(96,89),(96,91),(96,104),(97,87),(97,92),(98,31),(98,88),(98,94),(99,102),(99,123),(100,104),(100,107),(100,119),(101,102),(101,110),(102,119),(103,106),(103,107),(104,108),(104,122),(105,27),(105,110),(105,123),(106,121),(107,121),(107,122),(108,120),(109,90),(110,106),(110,119),(111,100),(111,103),(111,110),(112,120),(113,52),(113,97),(113,118),(114,53),(114,82),(114,83),(115,45),(115,66),(115,116),(116,43),(116,85),(116,113),(117,48),(117,80),(117,82),(117,88),(118,36),(118,71),(118,92),(119,108),(119,121),(121,120),(122,120),(123,81),(123,89),(123,119)],124)
 => ? = 1
[[1,2,3,4,5],[6]]
 => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4,5],[6]]
 => ([(0,1),(1,3),(1,4),(2,46),(3,8),(3,44),(4,9),(4,44),(5,51),(6,50),(7,6),(7,54),(8,7),(8,52),(9,5),(9,53),(10,37),(10,47),(11,34),(11,45),(12,35),(12,36),(13,20),(13,48),(14,19),(14,49),(15,77),(16,74),(17,11),(17,82),(17,84),(18,63),(18,71),(19,62),(20,2),(20,67),(21,57),(21,73),(22,75),(22,84),(23,69),(24,63),(24,65),(25,61),(25,64),(26,66),(26,72),(27,18),(27,57),(27,76),(28,19),(28,78),(29,23),(29,60),(30,25),(30,82),(30,83),(31,28),(31,55),(32,16),(32,60),(33,15),(33,55),(34,16),(34,59),(35,13),(35,38),(35,58),(36,10),(36,41),(36,58),(37,14),(37,28),(37,56),(38,20),(38,70),(39,40),(39,70),(40,15),(40,68),(41,31),(41,37),(41,81),(42,39),(42,43),(42,58),(43,33),(43,40),(43,81),(44,12),(44,52),(44,53),(45,18),(45,24),(45,59),(46,29),(46,32),(47,17),(47,22),(47,56),(48,17),(48,30),(48,67),(49,21),(49,27),(49,62),(50,31),(50,33),(51,38),(51,39),(52,36),(52,42),(52,54),(53,35),(53,42),(53,51),(54,41),(54,43),(54,50),(55,25),(55,77),(55,78),(56,49),(56,75),(56,78),(56,82),(57,26),(57,71),(57,86),(58,47),(58,48),(58,70),(58,81),(59,65),(59,71),(59,74),(60,26),(60,69),(60,74),(61,24),(61,76),(61,89),(62,73),(62,76),(63,88),(64,23),(64,89),(65,80),(65,88),(66,87),(67,46),(67,83),(67,84),(68,75),(68,77),(68,83),(69,66),(69,80),(70,22),(70,67),(70,68),(71,72),(71,88),(72,87),(73,86),(74,72),(74,80),(75,21),(75,79),(75,85),(76,63),(76,86),(77,64),(77,79),(78,61),(78,62),(78,79),(79,73),(79,89),(80,87),(81,30),(81,55),(81,56),(81,68),(82,27),(82,45),(82,61),(82,85),(83,29),(83,64),(83,85),(84,32),(84,34),(84,85),(85,57),(85,59),(85,60),(85,89),(86,66),(86,88),(88,87),(89,65),(89,69),(89,86)],90)
 => ? = 1
[[1,3,5,6],[2,4]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,5,6],[2,4]]
 => ([(0,1),(0,2),(1,6),(1,8),(2,5),(2,9),(3,60),(4,48),(5,38),(6,45),(7,17),(7,61),(8,18),(8,45),(9,14),(9,15),(9,38),(10,50),(10,65),(11,52),(11,53),(12,51),(12,66),(13,35),(13,67),(14,21),(14,64),(14,69),(15,68),(15,69),(16,34),(16,49),(17,33),(17,63),(18,20),(18,62),(18,68),(19,44),(19,58),(20,40),(20,56),(21,19),(21,54),(21,70),(22,74),(23,73),(23,75),(24,78),(24,91),(25,79),(26,81),(26,82),(27,78),(27,85),(28,90),(29,80),(30,82),(30,89),(31,81),(31,88),(32,83),(33,93),(34,3),(34,75),(35,84),(36,27),(36,76),(36,77),(37,34),(38,7),(38,64),(39,29),(39,95),(40,37),(41,51),(41,87),(42,24),(42,74),(43,24),(43,73),(43,77),(44,55),(45,4),(45,62),(46,28),(46,79),(47,35),(47,85),(48,16),(48,37),(49,39),(49,75),(50,22),(50,94),(51,25),(51,86),(52,12),(52,41),(52,76),(53,13),(53,47),(53,76),(54,44),(54,72),(55,27),(55,47),(56,33),(56,59),(57,42),(57,43),(57,94),(58,22),(58,42),(59,23),(59,43),(59,93),(60,25),(60,46),(61,11),(61,63),(61,72),(62,40),(62,48),(63,36),(63,52),(63,93),(64,54),(64,61),(65,23),(65,49),(65,94),(66,26),(66,31),(66,86),(67,26),(67,30),(67,84),(68,56),(68,71),(69,10),(69,70),(69,71),(70,50),(70,57),(70,58),(71,57),(71,59),(71,65),(72,36),(72,53),(72,55),(73,91),(73,95),(74,29),(74,91),(75,60),(75,95),(76,66),(76,67),(76,85),(76,87),(77,78),(77,87),(78,92),(79,32),(79,90),(80,28),(81,96),(82,32),(82,96),(84,81),(84,89),(85,31),(85,84),(85,92),(86,79),(86,82),(86,88),(87,30),(87,86),(87,92),(88,90),(88,96),(89,96),(90,83),(91,80),(92,88),(92,89),(93,41),(93,77),(94,39),(94,73),(94,74),(95,46),(95,80),(96,83)],97)
 => ? = 4
[[1,2,5,6],[3,4]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,5,6],[3,4]]
 => ([(0,2),(0,3),(1,4),(2,6),(2,8),(3,1),(4,5),(4,51),(5,43),(6,32),(7,14),(7,49),(8,11),(8,13),(8,32),(9,39),(9,52),(10,40),(10,53),(11,51),(11,54),(12,27),(12,57),(13,15),(13,50),(13,54),(14,16),(14,38),(14,56),(15,17),(15,44),(15,45),(16,19),(16,47),(17,28),(17,29),(18,72),(18,73),(19,68),(20,62),(21,66),(21,67),(22,58),(22,76),(23,65),(24,58),(24,67),(24,77),(25,66),(25,75),(26,63),(26,64),(27,69),(28,46),(29,34),(30,37),(30,61),(31,18),(31,59),(31,74),(32,7),(32,50),(33,27),(33,60),(34,20),(35,18),(35,60),(35,62),(36,39),(36,59),(36,64),(37,20),(37,70),(38,19),(38,61),(39,23),(39,71),(40,12),(40,33),(40,81),(41,34),(41,37),(42,30),(42,41),(43,30),(43,38),(44,29),(44,41),(45,28),(45,55),(46,33),(46,35),(47,31),(47,36),(47,68),(48,31),(48,35),(48,70),(48,81),(49,10),(49,55),(49,56),(50,45),(50,49),(51,42),(51,43),(52,21),(52,25),(52,71),(53,9),(53,26),(53,36),(53,81),(54,42),(54,44),(55,40),(55,46),(55,48),(56,47),(56,48),(56,53),(56,61),(57,21),(57,22),(57,24),(57,69),(58,80),(58,84),(59,24),(59,71),(59,73),(59,86),(60,25),(60,69),(60,73),(60,79),(61,26),(61,68),(61,70),(62,72),(62,79),(63,22),(63,79),(63,86),(64,23),(64,86),(65,78),(65,80),(66,85),(67,80),(67,85),(68,64),(68,74),(69,66),(69,76),(69,77),(70,62),(70,63),(70,74),(71,65),(71,67),(71,75),(72,82),(73,75),(73,77),(73,82),(74,72),(74,86),(75,78),(75,85),(76,84),(77,84),(77,85),(78,83),(79,76),(79,82),(80,83),(81,52),(81,57),(81,59),(81,60),(81,63),(82,78),(82,84),(84,83),(85,83),(86,58),(86,65),(86,82)],87)
 => ? = 4
[[1,3,4,6],[2,5]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4,6],[2,5]]
 => ([(0,2),(0,3),(1,6),(1,17),(2,9),(2,10),(3,1),(4,54),(5,55),(6,7),(6,61),(7,8),(7,63),(8,51),(9,4),(9,58),(10,16),(10,58),(11,33),(11,60),(12,47),(12,48),(13,49),(13,59),(14,44),(14,45),(15,32),(15,46),(16,18),(16,62),(16,65),(17,61),(17,62),(18,36),(18,50),(19,31),(19,38),(19,39),(20,78),(21,66),(22,69),(23,75),(23,84),(24,67),(25,85),(26,71),(27,70),(27,80),(28,76),(28,79),(29,67),(29,69),(30,12),(30,85),(31,14),(31,83),(31,84),(32,5),(32,82),(33,72),(34,22),(35,21),(35,82),(36,52),(37,31),(37,66),(38,57),(38,84),(39,30),(39,83),(40,33),(40,74),(41,20),(41,74),(42,20),(42,75),(43,48),(43,70),(43,76),(44,56),(45,34),(46,19),(46,37),(46,82),(47,22),(47,77),(48,26),(48,77),(49,11),(49,40),(49,68),(50,21),(50,37),(51,40),(51,41),(52,23),(52,42),(53,41),(53,42),(53,68),(54,32),(54,35),(55,25),(55,30),(56,24),(56,29),(57,27),(57,43),(57,73),(58,15),(58,54),(58,65),(59,23),(59,38),(59,68),(60,28),(60,43),(60,72),(61,13),(61,63),(61,64),(62,36),(62,64),(63,49),(63,51),(63,53),(64,52),(64,53),(64,59),(65,35),(65,46),(65,50),(66,25),(66,83),(67,81),(68,57),(68,60),(68,74),(68,75),(69,81),(70,26),(70,86),(71,81),(72,70),(72,79),(73,56),(73,76),(73,80),(74,27),(74,72),(74,78),(75,28),(75,73),(75,78),(76,29),(76,77),(76,86),(77,69),(77,71),(78,79),(78,80),(79,86),(80,24),(80,86),(82,39),(82,55),(82,66),(83,45),(83,85),(84,44),(84,73),(85,34),(85,47),(86,67),(86,71)],87)
 => ? = 5
[[1,2,4,6],[3,5]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4,6],[3,5]]
 => ([(0,2),(0,3),(1,4),(1,16),(2,1),(3,9),(3,10),(3,11),(4,6),(4,87),(5,86),(6,5),(6,88),(7,8),(7,84),(8,66),(8,81),(9,19),(9,82),(9,83),(10,20),(10,69),(10,83),(11,69),(11,82),(12,64),(12,67),(13,63),(13,65),(14,23),(14,78),(14,80),(15,18),(15,38),(15,68),(16,17),(16,79),(16,87),(17,46),(17,71),(18,47),(18,49),(19,42),(19,75),(20,76),(20,79),(21,31),(21,58),(21,59),(22,56),(22,57),(22,60),(23,27),(23,44),(23,45),(24,90),(25,93),(25,118),(26,91),(26,93),(27,92),(27,98),(28,94),(28,100),(28,101),(29,92),(29,95),(30,117),(31,89),(31,99),(32,100),(32,102),(33,96),(34,108),(35,109),(36,101),(36,103),(37,105),(38,14),(38,117),(39,55),(40,31),(40,91),(40,118),(41,32),(41,97),(42,39),(43,64),(43,96),(44,43),(44,98),(45,77),(45,92),(46,66),(46,116),(47,63),(47,112),(48,33),(49,51),(49,112),(50,35),(50,95),(51,27),(51,90),(52,29),(52,115),(53,26),(53,111),(53,114),(54,25),(54,111),(54,113),(55,24),(55,112),(56,52),(56,114),(57,78),(57,113),(58,61),(58,99),(59,74),(59,89),(60,21),(60,40),(60,113),(60,114),(61,36),(61,106),(62,12),(62,43),(63,48),(64,37),(64,94),(65,62),(66,73),(67,34),(67,94),(68,13),(68,47),(68,117),(69,7),(69,72),(70,54),(70,57),(70,116),(71,53),(71,56),(71,116),(72,39),(72,84),(73,29),(73,50),(74,28),(74,67),(74,97),(75,30),(75,68),(76,30),(76,38),(77,28),(77,32),(77,107),(78,45),(78,85),(79,46),(79,70),(80,44),(80,62),(81,24),(81,51),(82,42),(82,72),(83,15),(83,75),(83,76),(84,49),(84,55),(84,81),(85,41),(85,74),(85,77),(86,25),(86,26),(86,40),(87,22),(87,70),(87,71),(87,88),(88,53),(88,54),(88,60),(88,86),(89,97),(90,33),(90,98),(91,99),(91,110),(92,107),(93,35),(93,110),(94,105),(94,108),(95,36),(95,107),(95,109),(96,37),(97,34),(97,100),(98,96),(99,106),(100,108),(100,119),(101,105),(101,119),(102,119),(103,119),(105,104),(106,103),(107,101),(107,102),(108,104),(109,102),(109,103),(110,106),(110,109),(111,50),(111,93),(111,115),(112,48),(112,90),(113,59),(113,85),(113,118),(114,58),(114,91),(114,115),(115,61),(115,95),(115,110),(116,52),(116,73),(116,111),(117,65),(117,80),(118,41),(118,89),(119,104)],120)
 => ? = 5
[[1,2,3,6],[4,5]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,6],[4,5]]
 => ([(0,2),(0,3),(1,4),(1,18),(2,1),(3,12),(3,13),(3,17),(4,8),(4,69),(5,6),(5,22),(6,46),(7,68),(8,7),(8,70),(9,14),(9,57),(10,15),(10,56),(11,64),(11,67),(12,53),(12,54),(13,53),(13,55),(14,51),(14,52),(15,34),(15,65),(16,33),(16,66),(17,19),(17,54),(17,55),(18,20),(18,63),(18,69),(19,42),(19,63),(20,37),(20,58),(21,45),(21,49),(21,50),(22,10),(23,79),(23,84),(24,78),(24,85),(25,75),(25,99),(26,75),(26,83),(27,78),(27,92),(28,88),(28,89),(29,79),(29,93),(30,94),(31,86),(31,87),(32,80),(32,81),(33,82),(34,74),(35,28),(36,27),(36,74),(36,77),(37,51),(37,73),(38,34),(39,30),(39,77),(40,33),(40,83),(40,99),(41,57),(42,22),(43,26),(43,72),(43,97),(44,25),(44,71),(44,97),(45,56),(45,71),(46,38),(47,28),(47,85),(47,91),(48,31),(48,84),(48,90),(49,16),(49,40),(49,71),(49,72),(50,11),(50,60),(50,72),(51,61),(52,38),(53,41),(54,5),(54,42),(55,9),(55,41),(56,62),(56,65),(57,46),(57,52),(58,43),(58,50),(58,73),(59,44),(59,45),(59,73),(60,36),(60,64),(60,98),(61,36),(61,39),(62,35),(62,47),(63,37),(63,59),(64,24),(64,27),(64,76),(65,24),(65,47),(65,74),(66,23),(66,48),(66,82),(67,23),(67,29),(67,76),(68,25),(68,26),(68,40),(69,21),(69,58),(69,59),(69,70),(70,43),(70,44),(70,49),(70,68),(71,62),(71,99),(72,66),(72,67),(72,83),(72,98),(73,60),(73,61),(73,97),(74,78),(74,91),(75,30),(75,95),(76,84),(76,85),(76,92),(76,93),(77,31),(77,91),(77,92),(77,94),(78,102),(79,101),(80,100),(81,100),(82,79),(82,90),(83,29),(83,82),(83,95),(84,32),(84,86),(84,101),(85,32),(85,88),(85,102),(86,81),(86,103),(87,103),(88,80),(88,104),(89,104),(90,87),(90,101),(91,89),(91,102),(92,86),(92,96),(92,102),(93,88),(93,96),(93,101),(94,87),(94,89),(94,96),(95,90),(95,93),(95,94),(96,103),(96,104),(97,39),(97,75),(97,98),(98,48),(98,76),(98,77),(98,95),(99,35),(101,80),(101,103),(102,81),(102,104),(103,100),(104,100)],105)
 => ? = 5
[[1,3,4,5],[2,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4,5],[2,6]]
 => ([(0,1),(1,4),(1,5),(2,41),(3,40),(4,6),(4,42),(5,7),(5,42),(6,8),(6,43),(7,9),(7,44),(8,35),(9,36),(10,33),(10,34),(11,23),(11,38),(12,24),(12,39),(13,29),(13,30),(14,53),(14,59),(15,52),(15,60),(16,50),(17,51),(18,55),(19,56),(20,54),(21,10),(21,52),(21,53),(22,45),(23,3),(23,47),(24,2),(24,48),(25,22),(25,57),(26,22),(26,58),(27,23),(27,57),(28,24),(28,58),(29,11),(29,27),(29,46),(30,12),(30,28),(30,46),(31,16),(31,55),(32,17),(32,56),(33,16),(33,49),(34,17),(34,49),(35,25),(35,27),(36,26),(36,28),(37,25),(37,26),(37,46),(38,14),(38,21),(38,47),(39,15),(39,21),(39,48),(40,18),(40,31),(41,19),(41,32),(42,13),(42,43),(42,44),(43,29),(43,35),(43,37),(44,30),(44,36),(44,37),(45,59),(45,60),(46,38),(46,39),(46,57),(46,58),(47,40),(47,52),(47,59),(48,41),(48,53),(48,60),(49,50),(49,51),(50,54),(51,54),(52,31),(52,33),(52,61),(53,32),(53,34),(53,61),(55,20),(55,50),(56,20),(56,51),(57,15),(57,45),(57,47),(58,14),(58,45),(58,48),(59,18),(59,61),(60,19),(60,61),(61,49),(61,55),(61,56)],62)
 => ? = 6
[[1,2,4,5],[3,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4,5],[3,6]]
 => ([(0,1),(1,10),(1,11),(1,12),(2,3),(2,64),(3,48),(4,7),(4,62),(5,52),(6,45),(6,46),(7,28),(7,59),(8,43),(8,44),(9,13),(9,27),(9,58),(10,15),(10,60),(10,61),(11,47),(11,60),(12,5),(12,47),(12,61),(13,30),(13,56),(14,34),(14,57),(15,14),(15,50),(15,63),(16,26),(16,39),(16,40),(17,83),(18,76),(19,68),(19,75),(20,65),(20,82),(21,69),(22,66),(23,72),(24,66),(24,69),(25,70),(25,71),(26,8),(26,79),(26,82),(27,4),(27,80),(28,73),(29,22),(30,33),(30,78),(31,25),(31,84),(32,36),(33,28),(33,67),(34,32),(35,19),(35,81),(36,18),(36,65),(37,17),(37,80),(38,18),(38,67),(39,31),(39,82),(40,42),(40,79),(41,46),(41,68),(41,71),(42,6),(42,41),(42,81),(43,29),(44,49),(45,21),(45,74),(46,23),(46,74),(47,2),(47,51),(48,33),(48,38),(49,21),(49,24),(50,34),(50,54),(51,54),(51,64),(52,27),(52,37),(53,36),(53,38),(53,78),(54,32),(54,53),(55,20),(55,26),(55,83),(56,20),(56,39),(56,78),(57,17),(57,55),(58,16),(58,55),(58,56),(58,80),(59,19),(59,41),(59,73),(60,50),(60,51),(61,9),(61,52),(61,63),(62,35),(62,42),(62,59),(63,37),(63,57),(63,58),(64,30),(64,48),(64,53),(65,76),(65,84),(66,77),(67,25),(67,73),(67,76),(68,24),(68,74),(68,85),(69,77),(70,22),(70,85),(71,23),(71,85),(72,77),(73,71),(73,75),(74,69),(74,72),(75,85),(76,70),(76,75),(78,31),(78,65),(78,67),(79,44),(79,81),(80,40),(80,62),(80,83),(81,45),(81,49),(81,68),(82,43),(82,84),(83,35),(83,79),(84,29),(84,70),(85,66),(85,72)],86)
 => ? = 6
[[1,2,3,5],[4,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,5],[4,6]]
 => ([(0,1),(1,10),(1,11),(1,12),(2,51),(3,5),(3,61),(4,15),(4,53),(5,60),(6,29),(6,56),(7,41),(7,55),(8,40),(8,54),(9,28),(9,42),(10,43),(10,44),(11,43),(11,57),(12,13),(12,44),(12,57),(13,14),(13,46),(13,59),(14,30),(14,45),(15,33),(15,34),(15,50),(16,63),(16,86),(17,62),(18,72),(18,81),(19,63),(19,69),(20,70),(21,75),(21,88),(22,76),(22,79),(23,71),(23,72),(24,82),(25,78),(26,71),(26,80),(27,73),(28,2),(28,88),(29,74),(30,49),(31,38),(31,62),(32,19),(32,66),(32,85),(33,35),(33,85),(34,16),(34,64),(34,85),(35,25),(35,68),(36,24),(36,70),(37,18),(37,67),(38,22),(38,75),(38,77),(39,22),(39,69),(39,86),(40,17),(40,87),(41,20),(41,65),(42,7),(42,52),(42,88),(43,3),(43,58),(44,4),(44,46),(45,17),(45,31),(46,30),(46,53),(47,31),(47,48),(47,87),(48,38),(48,39),(48,64),(48,66),(49,21),(49,28),(50,21),(50,42),(50,64),(51,20),(51,36),(52,37),(52,55),(52,89),(53,9),(53,49),(53,50),(54,32),(54,33),(54,87),(55,18),(55,23),(55,65),(56,23),(56,26),(56,74),(57,8),(57,58),(57,59),(58,47),(58,54),(58,61),(59,40),(59,45),(59,47),(60,16),(60,19),(60,39),(61,32),(61,34),(61,48),(61,60),(62,25),(62,77),(63,29),(63,83),(64,52),(64,75),(64,86),(65,70),(65,71),(65,81),(66,68),(66,69),(66,77),(67,24),(67,81),(68,56),(68,78),(68,83),(69,79),(69,83),(70,27),(70,82),(71,27),(71,90),(72,90),(74,72),(74,80),(75,76),(75,89),(76,67),(77,78),(77,79),(78,26),(78,84),(79,84),(80,90),(81,82),(81,90),(82,73),(83,74),(83,84),(84,80),(85,6),(85,63),(85,68),(86,37),(86,76),(87,35),(87,62),(87,66),(88,41),(88,51),(88,89),(89,36),(89,65),(89,67),(90,73)],91)
 => ? = 6
[[1,2,3,4],[5,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,4],[5,6]]
 => ([(0,1),(1,11),(1,12),(1,13),(2,41),(3,5),(3,59),(4,15),(4,35),(5,57),(6,46),(7,27),(7,58),(8,43),(8,51),(9,42),(9,52),(10,26),(10,53),(11,45),(11,54),(12,44),(12,45),(13,14),(13,44),(13,54),(14,6),(14,28),(14,56),(15,32),(15,33),(15,34),(16,81),(17,61),(17,62),(18,62),(18,89),(19,68),(19,79),(20,67),(20,68),(21,77),(21,78),(22,63),(22,82),(23,70),(23,80),(24,63),(24,67),(24,83),(25,66),(26,73),(27,72),(28,35),(29,19),(30,17),(30,88),(30,90),(31,16),(31,61),(31,89),(32,41),(32,60),(33,49),(33,88),(34,18),(34,60),(34,88),(35,2),(35,32),(36,21),(36,71),(36,76),(37,26),(37,74),(38,39),(38,74),(39,16),(39,69),(40,42),(40,70),(40,71),(41,9),(41,50),(42,25),(42,75),(43,10),(43,37),(43,65),(44,4),(44,28),(45,3),(45,55),(46,37),(46,38),(47,38),(47,48),(47,65),(48,31),(48,39),(48,60),(48,90),(49,23),(49,40),(49,64),(50,29),(50,52),(51,30),(51,33),(51,65),(52,19),(52,20),(52,75),(53,36),(53,40),(53,73),(54,8),(54,55),(54,56),(55,47),(55,51),(55,59),(56,43),(56,46),(56,47),(57,17),(57,18),(57,31),(58,20),(58,22),(58,24),(58,72),(59,30),(59,34),(59,48),(59,57),(60,50),(60,89),(61,21),(61,81),(61,86),(62,27),(62,86),(63,87),(63,93),(64,58),(64,71),(64,80),(64,86),(65,49),(65,53),(65,74),(65,90),(66,84),(66,87),(67,87),(67,94),(68,94),(69,76),(69,80),(69,81),(70,25),(70,95),(71,24),(71,75),(71,77),(71,95),(72,68),(72,82),(72,83),(73,70),(73,76),(74,23),(74,69),(74,73),(75,66),(75,67),(75,79),(76,78),(76,95),(77,79),(77,83),(77,91),(78,91),(79,84),(79,94),(80,22),(80,85),(80,95),(81,78),(81,85),(82,93),(83,93),(83,94),(84,92),(85,82),(85,91),(86,72),(86,77),(86,85),(87,92),(88,7),(88,62),(88,64),(89,29),(90,36),(90,61),(90,64),(90,69),(91,84),(91,93),(93,92),(94,92),(95,63),(95,66),(95,91)],96)
 => ? = 6
[[1,4,5,6],[2],[3]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => [[1,4,5,6],[2],[3]]
 => ([(0,1),(1,4),(1,5),(2,34),(3,33),(4,7),(4,35),(5,8),(5,35),(6,9),(6,37),(7,6),(7,36),(8,32),(9,31),(10,25),(10,27),(11,15),(11,29),(12,19),(12,26),(13,38),(14,41),(15,39),(16,41),(17,40),(18,2),(18,47),(19,3),(19,45),(20,13),(20,46),(21,17),(21,47),(22,20),(22,45),(23,28),(23,38),(24,14),(24,43),(25,18),(25,44),(26,10),(26,30),(26,45),(27,11),(27,28),(27,44),(28,15),(28,42),(29,24),(29,39),(30,23),(30,27),(30,46),(31,13),(31,23),(32,19),(32,22),(33,18),(33,21),(34,14),(34,16),(35,12),(35,32),(35,36),(36,22),(36,26),(36,37),(37,20),(37,30),(37,31),(38,17),(38,42),(39,43),(40,16),(40,43),(42,39),(42,40),(43,41),(44,29),(44,42),(44,47),(45,25),(45,33),(45,46),(46,21),(46,38),(46,44),(47,24),(47,34),(47,40)],48)
 => ? = 1
[[1,3,5,6],[2],[4]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => [[1,3,5,6],[2],[4]]
 => ([(0,5),(0,6),(1,49),(2,38),(3,4),(3,53),(4,7),(4,12),(4,55),(5,33),(6,3),(6,11),(6,33),(7,42),(7,50),(8,29),(8,39),(9,28),(9,41),(10,15),(10,40),(10,52),(11,14),(11,51),(11,53),(12,13),(12,42),(12,54),(13,17),(13,45),(14,30),(14,44),(15,31),(15,43),(16,21),(16,25),(16,26),(17,71),(18,74),(19,58),(19,70),(20,73),(21,58),(21,72),(22,63),(23,64),(24,56),(24,68),(25,62),(25,72),(26,58),(26,62),(27,61),(27,67),(28,59),(29,1),(29,56),(30,32),(31,20),(31,57),(32,29),(33,2),(33,51),(34,47),(34,67),(35,27),(35,66),(35,68),(36,23),(36,73),(37,18),(37,69),(38,8),(38,32),(39,37),(39,56),(40,31),(40,75),(41,10),(41,48),(41,59),(42,17),(42,60),(43,19),(43,21),(43,57),(44,28),(44,46),(45,27),(45,34),(45,71),(46,24),(46,35),(46,59),(47,19),(47,26),(47,65),(48,34),(48,52),(48,66),(49,20),(49,36),(50,24),(50,39),(50,60),(51,30),(51,38),(52,16),(52,43),(52,47),(52,75),(53,9),(53,44),(53,55),(54,35),(54,45),(54,48),(54,60),(55,41),(55,46),(55,50),(55,54),(56,49),(56,69),(57,70),(57,72),(57,73),(58,76),(59,40),(59,66),(60,37),(60,68),(60,71),(61,74),(62,76),(64,63),(65,62),(65,70),(66,67),(66,75),(67,65),(68,61),(68,69),(69,36),(69,74),(70,64),(70,76),(71,18),(71,61),(72,22),(72,76),(73,22),(73,64),(74,23),(75,25),(75,57),(75,65),(76,63)],77)
 => ? = 1
[[1,2,5,6],[3],[4]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => [[1,2,5,6],[3],[4]]
 => ([(0,11),(0,12),(1,2),(2,8),(3,10),(3,45),(4,44),(5,18),(5,60),(6,19),(6,58),(7,17),(7,28),(8,9),(8,59),(9,52),(10,14),(10,20),(10,61),(11,1),(11,43),(12,3),(12,15),(12,43),(13,24),(13,42),(14,16),(14,55),(14,56),(15,39),(15,45),(16,29),(16,30),(17,53),(17,59),(18,31),(18,50),(19,23),(19,54),(20,41),(20,53),(20,56),(21,68),(22,65),(22,68),(23,64),(24,62),(25,62),(25,65),(26,70),(27,67),(28,6),(29,33),(29,73),(30,36),(30,73),(31,27),(31,72),(32,26),(32,69),(33,34),(34,21),(35,21),(35,66),(36,48),(37,22),(38,22),(38,66),(38,72),(39,28),(40,35),(40,64),(41,58),(41,63),(42,32),(42,62),(43,7),(43,39),(44,5),(44,49),(45,4),(45,61),(46,33),(46,51),(47,40),(47,51),(48,24),(48,25),(49,36),(49,60),(50,25),(50,42),(50,72),(51,34),(51,35),(52,23),(52,40),(53,46),(53,47),(54,31),(54,38),(54,64),(55,30),(55,49),(55,63),(56,29),(56,46),(56,63),(57,37),(57,38),(58,54),(58,57),(59,47),(59,52),(60,13),(60,48),(60,50),(61,41),(61,44),(61,55),(62,69),(63,57),(63,73),(64,27),(64,66),(65,69),(65,71),(66,67),(66,68),(67,26),(67,71),(68,71),(69,70),(71,70),(72,32),(72,65),(72,67),(73,37)],74)
 => ? = 1
[[1,3,4,6],[2],[5]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3,4,6],[2],[5]]
 => ([(0,5),(0,6),(1,4),(1,56),(2,50),(3,49),(4,9),(4,13),(4,58),(5,3),(5,53),(6,1),(6,8),(6,53),(7,44),(7,45),(8,15),(8,56),(8,59),(9,46),(9,54),(10,30),(10,57),(11,41),(11,42),(12,29),(12,43),(13,14),(13,46),(13,55),(14,37),(14,38),(15,33),(15,47),(16,28),(16,35),(16,36),(17,72),(18,60),(19,63),(20,68),(20,78),(21,61),(22,79),(23,65),(24,64),(24,74),(25,70),(25,73),(26,61),(26,63),(27,7),(27,79),(28,11),(28,77),(28,78),(29,2),(29,76),(30,66),(31,19),(32,18),(32,76),(33,48),(34,28),(34,60),(35,52),(35,78),(36,27),(36,77),(37,17),(37,69),(38,30),(38,69),(39,17),(39,68),(40,45),(40,64),(40,70),(41,51),(42,31),(43,16),(43,34),(43,76),(44,19),(44,71),(45,23),(45,71),(46,10),(46,38),(46,62),(47,18),(47,34),(48,20),(48,39),(49,29),(49,32),(50,22),(50,27),(51,21),(51,26),(52,24),(52,40),(52,67),(53,12),(53,49),(53,59),(54,20),(54,35),(54,62),(55,37),(55,39),(55,62),(56,33),(56,58),(57,25),(57,40),(57,66),(58,48),(58,54),(58,55),(59,32),(59,43),(59,47),(60,22),(60,77),(61,75),(62,52),(62,57),(62,68),(62,69),(63,75),(64,23),(64,80),(65,75),(66,64),(66,73),(67,51),(67,70),(67,74),(68,25),(68,67),(68,72),(69,24),(69,66),(69,72),(70,26),(70,71),(70,80),(71,63),(71,65),(72,73),(72,74),(73,80),(74,21),(74,80),(76,36),(76,50),(76,60),(77,42),(77,79),(78,41),(78,67),(79,31),(79,44),(80,61),(80,65)],81)
 => ? = 1
[[1,2,4,6],[3],[5]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2,4,6],[3],[5]]
 => ([(0,5),(0,6),(1,4),(1,56),(2,3),(2,55),(3,12),(3,34),(4,11),(4,17),(4,58),(5,2),(5,14),(5,66),(6,1),(6,13),(6,66),(7,49),(7,52),(8,50),(8,51),(9,19),(9,33),(9,57),(10,20),(10,67),(10,68),(11,16),(11,54),(11,72),(12,15),(12,53),(12,69),(13,56),(13,71),(14,55),(14,70),(15,23),(15,61),(16,22),(16,60),(17,42),(17,62),(17,72),(18,24),(18,40),(18,41),(19,36),(19,62),(19,69),(20,25),(20,35),(20,46),(21,95),(22,96),(23,80),(24,77),(24,78),(25,79),(25,86),(26,83),(26,84),(27,76),(27,84),(27,85),(28,82),(28,85),(29,82),(29,83),(30,91),(31,90),(32,81),(33,10),(33,95),(34,53),(35,64),(35,79),(36,49),(36,93),(37,32),(38,44),(38,77),(39,63),(39,79),(40,65),(40,78),(41,43),(41,77),(42,68),(42,94),(43,28),(43,87),(44,29),(44,87),(45,51),(45,81),(46,45),(46,86),(47,26),(47,88),(48,8),(48,45),(49,37),(50,30),(50,76),(51,31),(51,76),(52,48),(53,23),(53,93),(54,22),(54,94),(55,34),(56,58),(57,7),(57,36),(57,95),(58,42),(58,54),(59,39),(59,75),(60,24),(60,38),(60,96),(61,25),(61,39),(61,80),(62,59),(62,73),(63,28),(63,29),(63,89),(64,26),(64,27),(64,89),(65,27),(65,50),(65,88),(66,9),(66,70),(66,71),(67,46),(67,48),(68,35),(68,74),(69,59),(69,61),(69,93),(70,21),(70,57),(71,21),(71,33),(72,18),(72,60),(72,73),(72,94),(73,38),(73,41),(73,75),(74,47),(74,64),(74,65),(75,43),(75,44),(75,63),(76,90),(76,91),(77,87),(78,88),(79,89),(80,32),(80,86),(81,31),(82,97),(83,97),(84,91),(84,97),(85,90),(85,97),(86,81),(87,82),(88,30),(88,84),(89,83),(89,85),(90,92),(91,92),(93,37),(93,80),(94,40),(94,74),(94,96),(95,52),(95,67),(96,47),(96,78),(97,92)],98)
 => ? = 1
[[1,2,3,6],[4],[5]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3,6],[4],[5]]
 => ([(0,11),(0,12),(1,2),(2,7),(2,16),(3,44),(4,46),(5,10),(5,47),(6,43),(7,9),(7,59),(8,20),(8,45),(9,52),(10,13),(10,50),(11,1),(11,42),(12,5),(12,15),(12,42),(13,19),(13,56),(13,57),(14,38),(14,53),(15,37),(15,47),(16,54),(16,59),(17,24),(17,41),(18,23),(18,55),(19,28),(19,29),(20,40),(20,54),(20,57),(21,67),(22,63),(22,67),(23,65),(24,64),(25,63),(25,64),(26,68),(27,70),(28,34),(28,73),(29,35),(29,73),(30,21),(30,66),(31,25),(32,22),(32,66),(32,72),(33,27),(33,69),(34,36),(35,51),(36,24),(37,45),(38,26),(38,72),(39,30),(39,65),(40,43),(40,62),(41,33),(41,64),(42,8),(42,37),(43,14),(43,58),(44,17),(44,36),(45,6),(45,40),(46,3),(46,48),(47,4),(47,50),(48,34),(48,44),(49,35),(49,61),(50,46),(50,56),(51,21),(51,22),(52,23),(52,39),(53,25),(53,41),(53,72),(54,49),(54,60),(55,32),(55,38),(55,65),(56,28),(56,48),(56,62),(57,29),(57,49),(57,62),(58,31),(58,53),(59,18),(59,52),(59,60),(60,39),(60,55),(60,61),(61,30),(61,32),(61,51),(62,58),(62,73),(63,69),(63,71),(64,69),(65,26),(65,66),(66,67),(66,68),(67,71),(68,27),(68,71),(69,70),(71,70),(72,33),(72,63),(72,68),(73,31)],74)
 => ? = 1
[[1],[2],[3],[4],[5],[6]]
 => [[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
 => [[1],[2],[3],[4],[5],[6]]
 => ([],1)
 => 1
Description
The number of connected components of the Hasse diagram for the poset.
Matching statistic: St001964
(load all 10 compositions to match this statistic)
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 25%
Values
[[1]]
 => [1] => ([],1)
 => 0 = 1 - 1
[[1,2]]
 => [1,2] => ([(0,1)],2)
 => 0 = 1 - 1
[[1],[2]]
 => [2,1] => ([(0,1)],2)
 => 0 = 1 - 1
[[1,2,3]]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 0 = 1 - 1
[[1,3],[2]]
 => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
[[1,2],[3]]
 => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
[[1],[2],[3]]
 => [3,2,1] => ([(0,2),(2,1)],3)
 => 0 = 1 - 1
[[1,2,3,4]]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[[1,3,4],[2]]
 => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ? = 1 - 1
[[1,2,4],[3]]
 => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 1 - 1
[[1,2,3],[4]]
 => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ? = 1 - 1
[[1,3],[2,4]]
 => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
 => ? = 4 - 1
[[1,2],[3,4]]
 => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => ? = 4 - 1
[[1,4],[2],[3]]
 => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ? = 1 - 1
[[1,3],[2],[4]]
 => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 1 - 1
[[1,2],[3],[4]]
 => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ? = 1 - 1
[[1],[2],[3],[4]]
 => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[[1,2,3,4,5]]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[[1,3,4,5],[2]]
 => [2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1 - 1
[[1,2,4,5],[3]]
 => [3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[[1,2,3,5],[4]]
 => [4,1,2,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[[1,2,3,4],[5]]
 => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1 - 1
[[1,3,5],[2,4]]
 => [2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => ? = 4 - 1
[[1,2,5],[3,4]]
 => [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => ? = 4 - 1
[[1,3,4],[2,5]]
 => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
 => ? = 5 - 1
[[1,2,4],[3,5]]
 => [3,5,1,2,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
 => ? = 5 - 1
[[1,2,3],[4,5]]
 => [4,5,1,2,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 5 - 1
[[1,4,5],[2],[3]]
 => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 1 - 1
[[1,3,5],[2],[4]]
 => [4,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1 - 1
[[1,2,5],[3],[4]]
 => [4,3,1,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 1 - 1
[[1,3,4],[2],[5]]
 => [5,2,1,3,4] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 1 - 1
[[1,2,4],[3],[5]]
 => [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1 - 1
[[1,2,3],[4],[5]]
 => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 1 - 1
[[1,4],[2,5],[3]]
 => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
 => ? = 5 - 1
[[1,3],[2,5],[4]]
 => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
 => ? = 5 - 1
[[1,2],[3,5],[4]]
 => [4,3,5,1,2] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 5 - 1
[[1,3],[2,4],[5]]
 => [5,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => ? = 4 - 1
[[1,2],[3,4],[5]]
 => [5,3,4,1,2] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 4 - 1
[[1,5],[2],[3],[4]]
 => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1 - 1
[[1,4],[2],[3],[5]]
 => [5,3,2,1,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[[1,3],[2],[4],[5]]
 => [5,4,2,1,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1 - 1
[[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[[1,3,4,5,6],[2]]
 => [2,1,3,4,5,6] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ? = 1 - 1
[[1,2,4,5,6],[3]]
 => [3,1,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1 - 1
[[1,2,3,5,6],[4]]
 => [4,1,2,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
 => ? = 1 - 1
[[1,2,3,4,6],[5]]
 => [5,1,2,3,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1 - 1
[[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ? = 1 - 1
[[1,3,5,6],[2,4]]
 => [2,4,1,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
 => ? = 4 - 1
[[1,2,5,6],[3,4]]
 => [3,4,1,2,5,6] => ([(0,2),(0,3),(0,4),(1,8),(1,9),(2,1),(2,10),(2,11),(3,6),(3,7),(3,11),(4,6),(4,7),(4,10),(6,14),(7,12),(7,14),(8,13),(8,15),(9,13),(9,15),(10,8),(10,12),(10,14),(11,9),(11,12),(11,14),(12,13),(12,15),(13,5),(14,15),(15,5)],16)
 => ? = 4 - 1
[[1,3,4,6],[2,5]]
 => [2,5,1,3,4,6] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
 => ? = 5 - 1
[[1,2,4,6],[3,5]]
 => [3,5,1,2,4,6] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
 => ? = 5 - 1
[[1,2,3,6],[4,5]]
 => [4,5,1,2,3,6] => ([(0,3),(0,4),(0,5),(1,14),(2,6),(2,8),(2,14),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,13),(6,15),(8,13),(8,15),(9,12),(9,14),(10,8),(10,12),(11,6),(11,12),(11,14),(12,13),(12,15),(13,7),(14,15),(15,7)],16)
 => ? = 5 - 1
[[1,3,4,5],[2,6]]
 => [2,6,1,3,4,5] => ([(0,2),(0,3),(0,4),(0,6),(1,15),(1,17),(2,12),(2,13),(3,7),(3,12),(4,8),(4,12),(4,13),(5,1),(5,10),(5,11),(5,14),(6,5),(6,7),(6,8),(6,13),(7,10),(7,16),(8,11),(8,14),(8,16),(10,15),(10,17),(11,15),(11,17),(12,16),(13,14),(13,16),(14,15),(14,17),(15,9),(16,17),(17,9)],18)
 => ? = 6 - 1
[[1,2,4,5],[3,6]]
 => [3,6,1,2,4,5] => ([(0,3),(0,4),(0,5),(0,6),(1,11),(1,18),(2,12),(2,17),(2,18),(3,7),(3,14),(4,1),(4,10),(4,13),(4,14),(5,2),(5,9),(5,13),(5,14),(6,7),(6,9),(6,10),(7,17),(9,15),(9,17),(10,15),(10,17),(10,18),(11,16),(11,19),(12,16),(12,19),(13,11),(13,12),(13,15),(13,18),(14,17),(14,18),(15,16),(15,19),(16,8),(17,19),(18,16),(18,19),(19,8)],20)
 => ? = 6 - 1
[[1,2,3,5],[4,6]]
 => [4,6,1,2,3,5] => ([(0,2),(0,3),(0,4),(0,6),(1,15),(1,17),(2,7),(2,14),(3,9),(3,14),(4,9),(4,10),(4,14),(5,1),(5,11),(5,12),(5,16),(6,5),(6,7),(6,10),(6,14),(7,11),(7,16),(9,13),(10,12),(10,13),(10,16),(11,15),(11,17),(12,15),(12,17),(13,17),(14,13),(14,16),(15,8),(16,15),(16,17),(17,8)],18)
 => ? = 6 - 1
[[1,2,3,4],[5,6]]
 => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
 => ? = 6 - 1
[[1,4,5,6],[2],[3]]
 => [3,2,1,4,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => ? = 1 - 1
[[1,3,5,6],[2],[4]]
 => [4,2,1,3,5,6] => ([(0,1),(0,2),(0,4),(0,5),(1,9),(1,16),(2,10),(2,16),(3,6),(3,7),(3,15),(4,9),(4,11),(4,16),(5,3),(5,10),(5,11),(5,16),(6,13),(7,13),(7,14),(9,12),(10,6),(10,15),(11,7),(11,12),(11,15),(12,14),(13,8),(14,8),(15,13),(15,14),(16,12),(16,15)],17)
 => ? = 1 - 1
[[1,2,5,6],[3],[4]]
 => [4,3,1,2,5,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
 => ? = 1 - 1
[[1,3,4,6],[2],[5]]
 => [5,2,1,3,4,6] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,17),(2,7),(2,13),(3,9),(3,11),(3,13),(4,1),(4,8),(4,11),(4,13),(5,7),(5,8),(5,9),(7,16),(8,12),(8,16),(8,17),(9,12),(9,16),(10,14),(11,10),(11,12),(11,17),(12,14),(12,15),(13,16),(13,17),(14,6),(15,6),(16,15),(17,14),(17,15)],18)
 => ? = 1 - 1
[[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
Description
The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.