Supplementary

Maximally inflected sextics

TableauWebPromotion orderCrossing numberDihedral orbits

1 2 3 10 
4 5 6 11 
7 8 9 12
123

[[1, 4, 5, 6], [2, 7, 8, 9], [3, 10, 11, 12]]
[[1, 2, 3, 4], [5, 6, 7, 11], [8, 9, 10, 12]]
[[1, 2, 6, 7], [3, 5, 9, 10], [4, 8, 11, 12]]
[[1, 3, 4, 5], [2, 6, 7, 8], [9, 10, 11, 12]]
[[1, 2, 3, 8], [4, 6, 7, 11], [5, 9, 10, 12]]
[[1, 2, 3, 4], [5, 7, 8, 9], [6, 10, 11, 12]]
[[1, 3, 4, 5], [2, 6, 9, 10], [7, 8, 11, 12]]
[[1, 2, 5, 6], [3, 4, 7, 11], [8, 9, 10, 12]]
[[1, 2, 3, 7], [4, 5, 6, 8], [9, 10, 11, 12]]
[[1, 3, 4, 8], [2, 6, 7, 9], [5, 10, 11, 12]]
[[1, 2, 5, 9], [3, 4, 8, 10], [6, 7, 11, 12]]


1 2 3 10 
4 5 7 11 
6 8 9 12
122

[[1, 4, 5, 7], [2, 6, 8, 9], [3, 10, 11, 12]]
[[1, 2, 3, 4], [5, 6, 8, 11], [7, 9, 10, 12]]
[[1, 2, 6, 8], [3, 5, 9, 10], [4, 7, 11, 12]]
[[1, 3, 4, 5], [2, 6, 7, 9], [8, 10, 11, 12]]
[[1, 2, 3, 9], [4, 6, 7, 11], [5, 8, 10, 12]]
[[1, 4, 5, 6], [2, 7, 8, 10], [3, 9, 11, 12]]
[[1, 2, 3, 4], [5, 7, 8, 10], [6, 9, 11, 12]]
[[1, 2, 6, 7], [3, 5, 9, 11], [4, 8, 10, 12]]
[[1, 3, 4, 5], [2, 6, 9, 11], [7, 8, 10, 12]]
[[1, 2, 3, 8], [4, 6, 7, 10], [5, 9, 11, 12]]
[[1, 2, 5, 6], [3, 4, 7, 10], [8, 9, 11, 12]]
[[1, 3, 4, 9], [2, 5, 8, 11], [6, 7, 10, 12]]
[[1, 3, 6, 7], [2, 5, 8, 11], [4, 9, 10, 12]]
[[1, 2, 4, 5], [3, 6, 9, 10], [7, 8, 11, 12]]
[[1, 2, 4, 8], [3, 6, 7, 9], [5, 10, 11, 12]]
[[1, 3, 5, 6], [2, 4, 7, 11], [8, 9, 10, 12]]
[[1, 3, 5, 9], [2, 4, 8, 10], [6, 7, 11, 12]]
[[1, 2, 4, 7], [3, 5, 6, 8], [9, 10, 11, 12]]
[[1, 2, 4, 10], [3, 5, 6, 11], [7, 8, 9, 12]]
[[1, 3, 5, 8], [2, 6, 7, 9], [4, 10, 11, 12]]
[[1, 2, 3, 5], [4, 6, 7, 11], [8, 9, 10, 12]]
[[1, 2, 6, 9], [3, 4, 8, 10], [5, 7, 11, 12]]
[[1, 3, 4, 6], [2, 5, 7, 8], [9, 10, 11, 12]]


1 2 3 10 
4 5 8 11 
6 7 9 12
121

[[1, 4, 6, 7], [2, 5, 8, 9], [3, 10, 11, 12]]
[[1, 2, 3, 4], [5, 6, 9, 11], [7, 8, 10, 12]]
[[1, 2, 7, 8], [3, 5, 9, 10], [4, 6, 11, 12]]
[[1, 3, 4, 5], [2, 6, 7, 10], [8, 9, 11, 12]]
[[1, 2, 3, 9], [4, 6, 8, 11], [5, 7, 10, 12]]
[[1, 4, 5, 6], [2, 7, 8, 11], [3, 9, 10, 12]]
[[1, 2, 3, 4], [5, 7, 9, 10], [6, 8, 11, 12]]
[[1, 2, 6, 7], [3, 5, 8, 9], [4, 10, 11, 12]]
[[1, 3, 4, 5], [2, 6, 8, 11], [7, 9, 10, 12]]
[[1, 3, 7, 8], [2, 4, 9, 10], [5, 6, 11, 12]]
[[1, 2, 5, 6], [3, 4, 7, 9], [8, 10, 11, 12]]
[[1, 2, 4, 9], [3, 5, 8, 11], [6, 7, 10, 12]]
[[1, 3, 6, 7], [2, 5, 8, 10], [4, 9, 11, 12]]
[[1, 2, 3, 5], [4, 6, 9, 10], [7, 8, 11, 12]]
[[1, 2, 7, 8], [3, 4, 9, 11], [5, 6, 10, 12]]
[[1, 3, 4, 6], [2, 5, 7, 11], [8, 9, 10, 12]]
[[1, 2, 3, 9], [4, 5, 8, 10], [6, 7, 11, 12]]
[[1, 2, 5, 7], [3, 4, 6, 8], [9, 10, 11, 12]]
[[1, 3, 4, 10], [2, 5, 6, 11], [7, 8, 9, 12]]
[[1, 3, 6, 8], [2, 5, 7, 9], [4, 10, 11, 12]]
[[1, 2, 4, 5], [3, 6, 7, 11], [8, 9, 10, 12]]
[[1, 2, 7, 9], [3, 4, 8, 10], [5, 6, 11, 12]]
[[1, 3, 5, 6], [2, 4, 7, 8], [9, 10, 11, 12]]


1 2 3 10 
4 6 7 11 
5 8 9 12
121

[[1, 4, 5, 8], [2, 6, 7, 9], [3, 10, 11, 12]]
[[1, 2, 3, 4], [5, 7, 8, 11], [6, 9, 10, 12]]
[[1, 2, 6, 9], [3, 5, 8, 10], [4, 7, 11, 12]]
[[1, 3, 4, 5], [2, 6, 8, 9], [7, 10, 11, 12]]
[[1, 4, 5, 6], [2, 7, 9, 10], [3, 8, 11, 12]]
[[1, 2, 6, 7], [3, 5, 8, 11], [4, 9, 10, 12]]
[[1, 2, 3, 8], [4, 6, 7, 9], [5, 10, 11, 12]]
[[1, 3, 4, 9], [2, 5, 8, 10], [6, 7, 11, 12]]
[[1, 2, 5, 10], [3, 4, 6, 11], [7, 8, 9, 12]]
[[1, 2, 3, 6], [4, 5, 7, 11], [8, 9, 10, 12]]
[[1, 3, 4, 7], [2, 5, 6, 8], [9, 10, 11, 12]]


1 2 3 10 
4 6 8 11 
5 7 9 12
120

[[1, 4, 6, 8], [2, 5, 7, 9], [3, 10, 11, 12]]
[[1, 2, 3, 4], [5, 7, 9, 11], [6, 8, 10, 12]]
[[1, 2, 7, 9], [3, 5, 8, 10], [4, 6, 11, 12]]
[[1, 3, 4, 5], [2, 6, 8, 10], [7, 9, 11, 12]]
[[1, 4, 5, 6], [2, 7, 9, 11], [3, 8, 10, 12]]
[[1, 2, 6, 7], [3, 5, 8, 10], [4, 9, 11, 12]]
[[1, 3, 7, 8], [2, 4, 9, 11], [5, 6, 10, 12]]
[[1, 2, 4, 9], [3, 5, 8, 10], [6, 7, 11, 12]]
[[1, 3, 5, 10], [2, 4, 6, 11], [7, 8, 9, 12]]
[[1, 2, 4, 6], [3, 5, 7, 11], [8, 9, 10, 12]]
[[1, 3, 5, 7], [2, 4, 6, 8], [9, 10, 11, 12]]


1 2 3 7 
4 5 6 11 
8 9 10 12
46

[[1, 3, 4, 5], [2, 7, 8, 9], [6, 10, 11, 12]]
[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
[[1, 2, 5, 6], [3, 4, 9, 10], [7, 8, 11, 12]]


1 2 3 9 
4 5 8 11 
6 7 10 12
62

[[1, 3, 6, 7], [2, 5, 8, 9], [4, 10, 11, 12]]
[[1, 2, 3, 4], [5, 6, 9, 10], [7, 8, 11, 12]]
[[1, 2, 7, 8], [3, 4, 9, 10], [5, 6, 11, 12]]
[[1, 3, 4, 5], [2, 6, 7, 11], [8, 9, 10, 12]]
[[1, 2, 5, 6], [3, 4, 7, 8], [9, 10, 11, 12]]


1 2 4 10 
3 5 8 11 
6 7 9 12
60

[[1, 4, 6, 7], [2, 5, 8, 10], [3, 9, 11, 12]]
[[1, 2, 3, 5], [4, 6, 9, 11], [7, 8, 10, 12]]
[[1, 2, 7, 8], [3, 5, 9, 11], [4, 6, 10, 12]]
[[1, 3, 4, 6], [2, 5, 7, 10], [8, 9, 11, 12]]
[[1, 2, 3, 9], [4, 6, 8, 10], [5, 7, 11, 12]]
[[1, 4, 5, 7], [2, 6, 8, 11], [3, 9, 10, 12]]
[[1, 3, 4, 10], [2, 5, 7, 11], [6, 8, 9, 12]]
[[1, 2, 6, 8], [3, 5, 7, 9], [4, 10, 11, 12]]
[[1, 2, 4, 5], [3, 6, 8, 11], [7, 9, 10, 12]]
[[1, 3, 7, 9], [2, 4, 8, 10], [5, 6, 11, 12]]
[[1, 3, 5, 6], [2, 4, 7, 9], [8, 10, 11, 12]]


1 2 4 10 
3 6 7 11 
5 8 9 12
122

[[1, 4, 5, 8], [2, 6, 7, 10], [3, 9, 11, 12]]
[[1, 2, 3, 5], [4, 7, 8, 11], [6, 9, 10, 12]]
[[1, 2, 6, 9], [3, 5, 8, 11], [4, 7, 10, 12]]
[[1, 3, 4, 6], [2, 5, 8, 9], [7, 10, 11, 12]]
[[1, 2, 3, 7], [4, 6, 9, 10], [5, 8, 11, 12]]
[[1, 4, 5, 7], [2, 6, 9, 10], [3, 8, 11, 12]]
[[1, 3, 4, 8], [2, 5, 7, 11], [6, 9, 10, 12]]
[[1, 2, 6, 8], [3, 5, 7, 11], [4, 9, 10, 12]]
[[1, 2, 4, 5], [3, 6, 8, 9], [7, 10, 11, 12]]
[[1, 2, 3, 7], [4, 6, 8, 9], [5, 10, 11, 12]]
[[1, 3, 5, 6], [2, 7, 9, 10], [4, 8, 11, 12]]
[[1, 3, 4, 8], [2, 5, 9, 10], [6, 7, 11, 12]]
[[1, 2, 6, 7], [3, 4, 8, 11], [5, 9, 10, 12]]
[[1, 2, 5, 9], [3, 4, 6, 11], [7, 8, 10, 12]]
[[1, 2, 3, 8], [4, 5, 7, 9], [6, 10, 11, 12]]
[[1, 2, 3, 6], [4, 5, 7, 10], [8, 9, 11, 12]]
[[1, 3, 4, 9], [2, 6, 8, 10], [5, 7, 11, 12]]
[[1, 3, 4, 7], [2, 6, 8, 11], [5, 9, 10, 12]]
[[1, 2, 5, 10], [3, 4, 7, 11], [6, 8, 9, 12]]
[[1, 2, 5, 8], [3, 4, 7, 9], [6, 10, 11, 12]]
[[1, 2, 3, 6], [4, 5, 8, 11], [7, 9, 10, 12]]
[[1, 3, 6, 9], [2, 5, 8, 10], [4, 7, 11, 12]]
[[1, 3, 4, 7], [2, 5, 6, 9], [8, 10, 11, 12]]


1 2 4 10 
3 6 8 11 
5 7 9 12
121

[[1, 4, 6, 8], [2, 5, 7, 10], [3, 9, 11, 12]]
[[1, 2, 3, 5], [4, 7, 9, 11], [6, 8, 10, 12]]
[[1, 2, 7, 9], [3, 5, 8, 11], [4, 6, 10, 12]]
[[1, 3, 4, 6], [2, 5, 8, 10], [7, 9, 11, 12]]
[[1, 2, 3, 8], [4, 6, 9, 10], [5, 7, 11, 12]]
[[1, 4, 5, 7], [2, 6, 9, 11], [3, 8, 10, 12]]
[[1, 3, 4, 9], [2, 5, 7, 11], [6, 8, 10, 12]]
[[1, 2, 6, 8], [3, 5, 7, 10], [4, 9, 11, 12]]
[[1, 2, 4, 5], [3, 6, 8, 10], [7, 9, 11, 12]]
[[1, 3, 7, 9], [2, 4, 8, 11], [5, 6, 10, 12]]
[[1, 3, 5, 6], [2, 7, 9, 11], [4, 8, 10, 12]]
[[1, 2, 4, 8], [3, 5, 9, 10], [6, 7, 11, 12]]
[[1, 2, 6, 7], [3, 4, 8, 10], [5, 9, 11, 12]]
[[1, 3, 5, 9], [2, 4, 6, 11], [7, 8, 10, 12]]
[[1, 3, 7, 8], [2, 5, 9, 11], [4, 6, 10, 12]]
[[1, 2, 4, 6], [3, 5, 7, 10], [8, 9, 11, 12]]
[[1, 2, 4, 9], [3, 6, 8, 10], [5, 7, 11, 12]]
[[1, 3, 5, 7], [2, 6, 8, 11], [4, 9, 10, 12]]
[[1, 3, 5, 10], [2, 4, 7, 11], [6, 8, 9, 12]]
[[1, 2, 6, 8], [3, 4, 7, 9], [5, 10, 11, 12]]
[[1, 2, 4, 6], [3, 5, 8, 11], [7, 9, 10, 12]]
[[1, 3, 7, 9], [2, 5, 8, 10], [4, 6, 11, 12]]
[[1, 3, 5, 7], [2, 4, 6, 9], [8, 10, 11, 12]]


1 2 5 10 
3 4 8 11 
6 7 9 12
123

[[1, 4, 6, 7], [2, 5, 9, 10], [3, 8, 11, 12]]
[[1, 2, 3, 6], [4, 5, 9, 11], [7, 8, 10, 12]]
[[1, 2, 5, 8], [3, 6, 7, 11], [4, 9, 10, 12]]
[[1, 3, 4, 7], [2, 5, 6, 10], [8, 9, 11, 12]]
[[1, 2, 3, 6], [4, 7, 8, 9], [5, 10, 11, 12]]
[[1, 4, 5, 8], [2, 6, 7, 11], [3, 9, 10, 12]]
[[1, 3, 4, 7], [2, 5, 9, 10], [6, 8, 11, 12]]
[[1, 2, 5, 6], [3, 7, 8, 9], [4, 10, 11, 12]]
[[1, 2, 5, 8], [3, 4, 6, 11], [7, 9, 10, 12]]
[[1, 3, 6, 7], [2, 4, 9, 10], [5, 8, 11, 12]]
[[1, 2, 3, 6], [4, 5, 7, 9], [8, 10, 11, 12]]
[[1, 2, 4, 8], [3, 5, 7, 11], [6, 9, 10, 12]]
[[1, 3, 4, 7], [2, 6, 8, 10], [5, 9, 11, 12]]
[[1, 2, 3, 5], [4, 6, 8, 9], [7, 10, 11, 12]]
[[1, 2, 5, 8], [3, 4, 9, 11], [6, 7, 10, 12]]
[[1, 3, 4, 6], [2, 7, 9, 10], [5, 8, 11, 12]]
[[1, 2, 3, 9], [4, 5, 6, 10], [7, 8, 11, 12]]
[[1, 2, 5, 7], [3, 4, 8, 11], [6, 9, 10, 12]]
[[1, 3, 4, 10], [2, 6, 7, 11], [5, 8, 9, 12]]
[[1, 2, 3, 8], [4, 5, 6, 9], [7, 10, 11, 12]]
[[1, 2, 4, 5], [3, 7, 8, 11], [6, 9, 10, 12]]
[[1, 3, 4, 9], [2, 6, 7, 10], [5, 8, 11, 12]]
[[1, 3, 5, 6], [2, 4, 8, 9], [7, 10, 11, 12]]


1 2 5 6 
3 4 9 11 
7 8 10 12
125

[[1, 3, 5, 6], [2, 4, 9, 10], [7, 8, 11, 12]]
[[1, 2, 3, 7], [4, 5, 6, 10], [8, 9, 11, 12]]
[[1, 2, 4, 7], [3, 5, 6, 11], [8, 9, 10, 12]]
[[1, 3, 4, 8], [2, 6, 7, 11], [5, 9, 10, 12]]
[[1, 2, 3, 5], [4, 6, 7, 8], [9, 10, 11, 12]]
[[1, 2, 4, 5], [3, 7, 8, 9], [6, 10, 11, 12]]
[[1, 3, 4, 6], [2, 7, 8, 9], [5, 10, 11, 12]]
[[1, 2, 5, 7], [3, 4, 9, 10], [6, 8, 11, 12]]
[[1, 2, 3, 8], [4, 5, 6, 11], [7, 9, 10, 12]]
[[1, 2, 3, 4], [5, 6, 7, 9], [8, 10, 11, 12]]
[[1, 3, 4, 5], [2, 7, 8, 10], [6, 9, 11, 12]]


1 2 5 8 
3 4 7 11 
6 9 10 12
34

[[1, 3, 4, 7], [2, 6, 9, 10], [5, 8, 11, 12]]
[[1, 2, 3, 6], [4, 5, 8, 9], [7, 10, 11, 12]]


1 2 5 9 
3 4 8 11 
6 7 10 12
124

[[1, 3, 6, 7], [2, 5, 9, 10], [4, 8, 11, 12]]
[[1, 2, 3, 6], [4, 5, 9, 10], [7, 8, 11, 12]]
[[1, 2, 4, 8], [3, 6, 7, 11], [5, 9, 10, 12]]
[[1, 3, 4, 7], [2, 5, 6, 11], [8, 9, 10, 12]]
[[1, 2, 3, 5], [4, 7, 8, 9], [6, 10, 11, 12]]
[[1, 2, 4, 5], [3, 6, 7, 8], [9, 10, 11, 12]]
[[1, 3, 4, 6], [2, 5, 9, 10], [7, 8, 11, 12]]
[[1, 3, 5, 6], [2, 7, 8, 9], [4, 10, 11, 12]]
[[1, 2, 5, 7], [3, 4, 6, 11], [8, 9, 10, 12]]
[[1, 2, 6, 7], [3, 4, 9, 10], [5, 8, 11, 12]]
[[1, 2, 3, 6], [4, 5, 7, 8], [9, 10, 11, 12]]
[[1, 2, 3, 8], [4, 5, 7, 11], [6, 9, 10, 12]]
[[1, 3, 4, 7], [2, 6, 8, 9], [5, 10, 11, 12]]
[[1, 2, 3, 4], [5, 6, 8, 9], [7, 10, 11, 12]]
[[1, 2, 5, 8], [3, 4, 9, 10], [6, 7, 11, 12]]
[[1, 3, 4, 5], [2, 7, 9, 10], [6, 8, 11, 12]]
[[1, 2, 3, 9], [4, 5, 6, 11], [7, 8, 10, 12]]
[[1, 2, 5, 6], [3, 4, 8, 11], [7, 9, 10, 12]]
[[1, 2, 3, 4], [5, 6, 7, 10], [8, 9, 11, 12]]
[[1, 2, 3, 7], [4, 5, 6, 9], [8, 10, 11, 12]]
[[1, 3, 4, 5], [2, 7, 8, 11], [6, 9, 10, 12]]
[[1, 3, 4, 8], [2, 6, 7, 10], [5, 9, 11, 12]]
[[1, 2, 5, 6], [3, 4, 8, 9], [7, 10, 11, 12]]


1 2 6 10 
3 4 8 11 
5 7 9 12
122

[[1, 4, 6, 8], [2, 5, 9, 10], [3, 7, 11, 12]]
[[1, 2, 3, 7], [4, 5, 9, 11], [6, 8, 10, 12]]
[[1, 2, 5, 9], [3, 6, 7, 11], [4, 8, 10, 12]]
[[1, 3, 4, 8], [2, 5, 6, 10], [7, 9, 11, 12]]
[[1, 2, 3, 6], [4, 7, 8, 10], [5, 9, 11, 12]]
[[1, 4, 5, 9], [2, 6, 7, 11], [3, 8, 10, 12]]
[[1, 3, 4, 7], [2, 5, 9, 11], [6, 8, 10, 12]]
[[1, 2, 5, 6], [3, 7, 8, 10], [4, 9, 11, 12]]
[[1, 2, 5, 8], [3, 4, 6, 10], [7, 9, 11, 12]]
[[1, 3, 6, 7], [2, 4, 9, 11], [5, 8, 10, 12]]
[[1, 3, 6, 9], [2, 5, 7, 11], [4, 8, 10, 12]]
[[1, 2, 4, 8], [3, 5, 7, 10], [6, 9, 11, 12]]
[[1, 2, 4, 7], [3, 6, 8, 10], [5, 9, 11, 12]]
[[1, 3, 5, 9], [2, 6, 8, 11], [4, 7, 10, 12]]
[[1, 3, 5, 8], [2, 4, 9, 11], [6, 7, 10, 12]]
[[1, 2, 4, 6], [3, 7, 9, 10], [5, 8, 11, 12]]
[[1, 2, 4, 9], [3, 5, 6, 10], [7, 8, 11, 12]]
[[1, 3, 5, 7], [2, 4, 8, 11], [6, 9, 10, 12]]
[[1, 3, 5, 10], [2, 6, 7, 11], [4, 8, 9, 12]]
[[1, 2, 4, 8], [3, 5, 6, 9], [7, 10, 11, 12]]
[[1, 2, 4, 6], [3, 7, 8, 11], [5, 9, 10, 12]]
[[1, 3, 5, 9], [2, 6, 7, 10], [4, 8, 11, 12]]
[[1, 3, 5, 7], [2, 4, 8, 9], [6, 10, 11, 12]]


1 2 6 10 
3 5 7 11 
4 8 9 12
40

[[1, 4, 5, 9], [2, 6, 8, 10], [3, 7, 11, 12]]
[[1, 2, 3, 7], [4, 6, 8, 11], [5, 9, 10, 12]]
[[1, 3, 4, 8], [2, 5, 7, 9], [6, 10, 11, 12]]


1 2 6 10 
3 5 8 11 
4 7 9 12
121

[[1, 4, 6, 9], [2, 5, 8, 10], [3, 7, 11, 12]]
[[1, 2, 3, 7], [4, 6, 9, 11], [5, 8, 10, 12]]
[[1, 2, 5, 10], [3, 6, 7, 11], [4, 8, 9, 12]]
[[1, 3, 4, 8], [2, 5, 7, 10], [6, 9, 11, 12]]
[[1, 2, 3, 6], [4, 7, 8, 11], [5, 9, 10, 12]]
[[1, 4, 5, 9], [2, 6, 8, 11], [3, 7, 10, 12]]
[[1, 3, 4, 7], [2, 5, 8, 9], [6, 10, 11, 12]]
[[1, 2, 5, 6], [3, 7, 9, 10], [4, 8, 11, 12]]
[[1, 4, 5, 8], [2, 6, 9, 10], [3, 7, 11, 12]]
[[1, 3, 6, 7], [2, 4, 8, 11], [5, 9, 10, 12]]
[[1, 2, 6, 9], [3, 5, 7, 11], [4, 8, 10, 12]]
[[1, 2, 4, 8], [3, 5, 7, 9], [6, 10, 11, 12]]
[[1, 2, 3, 7], [4, 6, 8, 10], [5, 9, 11, 12]]
[[1, 3, 5, 9], [2, 6, 8, 10], [4, 7, 11, 12]]
[[1, 3, 4, 8], [2, 5, 9, 11], [6, 7, 10, 12]]
[[1, 2, 6, 10], [3, 4, 7, 11], [5, 8, 9, 12]]
[[1, 2, 5, 9], [3, 4, 6, 10], [7, 8, 11, 12]]
[[1, 2, 3, 7], [4, 5, 8, 11], [6, 9, 10, 12]]
[[1, 3, 6, 10], [2, 5, 7, 11], [4, 8, 9, 12]]
[[1, 3, 4, 8], [2, 5, 6, 9], [7, 10, 11, 12]]
[[1, 2, 4, 7], [3, 6, 8, 11], [5, 9, 10, 12]]
[[1, 4, 5, 9], [2, 6, 7, 10], [3, 8, 11, 12]]
[[1, 3, 5, 8], [2, 4, 7, 9], [6, 10, 11, 12]]


1 2 6 9 
3 4 8 11 
5 7 10 12
123

[[1, 3, 6, 8], [2, 5, 9, 10], [4, 7, 11, 12]]
[[1, 2, 3, 7], [4, 5, 9, 10], [6, 8, 11, 12]]
[[1, 2, 4, 9], [3, 6, 7, 11], [5, 8, 10, 12]]
[[1, 3, 4, 8], [2, 5, 6, 11], [7, 9, 10, 12]]
[[1, 2, 3, 5], [4, 7, 8, 10], [6, 9, 11, 12]]
[[1, 2, 4, 5], [3, 6, 7, 9], [8, 10, 11, 12]]
[[1, 3, 4, 6], [2, 5, 9, 11], [7, 8, 10, 12]]
[[1, 3, 5, 6], [2, 7, 8, 10], [4, 9, 11, 12]]
[[1, 2, 5, 7], [3, 4, 6, 10], [8, 9, 11, 12]]
[[1, 2, 6, 7], [3, 4, 9, 11], [5, 8, 10, 12]]
[[1, 3, 6, 8], [2, 5, 7, 11], [4, 9, 10, 12]]
[[1, 2, 3, 8], [4, 5, 7, 10], [6, 9, 11, 12]]
[[1, 2, 4, 7], [3, 6, 8, 9], [5, 10, 11, 12]]
[[1, 3, 4, 9], [2, 6, 8, 11], [5, 7, 10, 12]]
[[1, 3, 5, 8], [2, 4, 9, 10], [6, 7, 11, 12]]
[[1, 2, 4, 5], [3, 7, 9, 10], [6, 8, 11, 12]]
[[1, 2, 4, 9], [3, 5, 6, 11], [7, 8, 10, 12]]
[[1, 3, 5, 6], [2, 4, 8, 11], [7, 9, 10, 12]]
[[1, 2, 3, 5], [4, 6, 7, 10], [8, 9, 11, 12]]
[[1, 2, 4, 7], [3, 5, 6, 9], [8, 10, 11, 12]]
[[1, 3, 4, 6], [2, 7, 8, 11], [5, 9, 10, 12]]
[[1, 3, 5, 8], [2, 6, 7, 10], [4, 9, 11, 12]]
[[1, 2, 5, 7], [3, 4, 8, 9], [6, 10, 11, 12]]


1 2 7 10 
3 4 8 11 
5 6 9 12
121

[[1, 4, 7, 8], [2, 5, 9, 10], [3, 6, 11, 12]]
[[1, 2, 3, 8], [4, 5, 9, 11], [6, 7, 10, 12]]
[[1, 2, 5, 9], [3, 6, 8, 11], [4, 7, 10, 12]]
[[1, 3, 4, 9], [2, 5, 6, 10], [7, 8, 11, 12]]
[[1, 2, 3, 6], [4, 7, 9, 10], [5, 8, 11, 12]]
[[1, 4, 5, 10], [2, 6, 7, 11], [3, 8, 9, 12]]
[[1, 3, 4, 7], [2, 5, 8, 11], [6, 9, 10, 12]]
[[1, 2, 5, 6], [3, 7, 8, 11], [4, 9, 10, 12]]
[[1, 2, 5, 8], [3, 4, 6, 9], [7, 10, 11, 12]]
[[1, 3, 6, 7], [2, 4, 8, 9], [5, 10, 11, 12]]
[[1, 3, 6, 9], [2, 5, 7, 10], [4, 8, 11, 12]]


1 2 7 10 
3 5 8 11 
4 6 9 12
120

[[1, 4, 7, 9], [2, 5, 8, 10], [3, 6, 11, 12]]
[[1, 2, 3, 8], [4, 6, 9, 11], [5, 7, 10, 12]]
[[1, 2, 5, 10], [3, 6, 8, 11], [4, 7, 9, 12]]
[[1, 3, 4, 9], [2, 5, 7, 10], [6, 8, 11, 12]]
[[1, 2, 3, 6], [4, 7, 9, 11], [5, 8, 10, 12]]
[[1, 4, 5, 10], [2, 6, 8, 11], [3, 7, 9, 12]]
[[1, 3, 4, 7], [2, 5, 8, 10], [6, 9, 11, 12]]
[[1, 2, 5, 6], [3, 7, 9, 11], [4, 8, 10, 12]]
[[1, 4, 5, 8], [2, 6, 9, 11], [3, 7, 10, 12]]
[[1, 3, 6, 7], [2, 4, 8, 10], [5, 9, 11, 12]]
[[1, 2, 6, 9], [3, 5, 7, 10], [4, 8, 11, 12]]
[[1, 4, 7, 8], [2, 5, 9, 11], [3, 6, 10, 12]]
[[1, 3, 7, 10], [2, 4, 8, 11], [5, 6, 9, 12]]
[[1, 2, 5, 9], [3, 6, 8, 10], [4, 7, 11, 12]]
[[1, 2, 4, 8], [3, 5, 9, 11], [6, 7, 10, 12]]
[[1, 3, 6, 10], [2, 4, 7, 11], [5, 8, 9, 12]]
[[1, 3, 5, 9], [2, 4, 6, 10], [7, 8, 11, 12]]
[[1, 2, 4, 7], [3, 5, 8, 11], [6, 9, 10, 12]]
[[1, 4, 6, 10], [2, 5, 7, 11], [3, 8, 9, 12]]
[[1, 3, 5, 8], [2, 4, 6, 9], [7, 10, 11, 12]]
[[1, 2, 5, 7], [3, 6, 8, 11], [4, 9, 10, 12]]
[[1, 4, 6, 9], [2, 5, 7, 10], [3, 8, 11, 12]]
[[1, 3, 6, 8], [2, 4, 7, 9], [5, 10, 11, 12]]


1 2 7 9 
3 4 8 11 
5 6 10 12
122

[[1, 3, 7, 8], [2, 5, 9, 10], [4, 6, 11, 12]]
[[1, 2, 3, 8], [4, 5, 9, 10], [6, 7, 11, 12]]
[[1, 2, 4, 9], [3, 6, 8, 11], [5, 7, 10, 12]]
[[1, 3, 4, 9], [2, 5, 6, 11], [7, 8, 10, 12]]
[[1, 2, 3, 5], [4, 7, 9, 10], [6, 8, 11, 12]]
[[1, 2, 4, 5], [3, 6, 7, 10], [8, 9, 11, 12]]
[[1, 3, 4, 6], [2, 5, 8, 11], [7, 9, 10, 12]]
[[1, 3, 5, 6], [2, 7, 8, 11], [4, 9, 10, 12]]
[[1, 2, 5, 7], [3, 4, 6, 9], [8, 10, 11, 12]]
[[1, 2, 6, 7], [3, 4, 8, 9], [5, 10, 11, 12]]
[[1, 3, 6, 8], [2, 5, 7, 10], [4, 9, 11, 12]]


1 3 4 10 
2 5 8 11 
6 7 9 12
121

[[1, 4, 6, 7], [2, 5, 8, 11], [3, 9, 10, 12]]
[[1, 2, 4, 5], [3, 6, 9, 11], [7, 8, 10, 12]]
[[1, 2, 5, 8], [3, 6, 7, 9], [4, 10, 11, 12]]
[[1, 3, 5, 6], [2, 4, 7, 10], [8, 9, 11, 12]]
[[1, 3, 6, 9], [2, 4, 8, 10], [5, 7, 11, 12]]
[[1, 2, 4, 10], [3, 5, 7, 11], [6, 8, 9, 12]]
[[1, 2, 3, 5], [4, 6, 8, 11], [7, 9, 10, 12]]
[[1, 3, 4, 6], [2, 5, 7, 9], [8, 10, 11, 12]]
[[1, 4, 5, 7], [2, 6, 8, 10], [3, 9, 11, 12]]
[[1, 2, 6, 8], [3, 5, 9, 11], [4, 7, 10, 12]]
[[1, 2, 3, 9], [4, 6, 7, 10], [5, 8, 11, 12]]


1 3 4 10 
2 6 8 11 
5 7 9 12
122

[[1, 4, 6, 8], [2, 5, 7, 11], [3, 9, 10, 12]]
[[1, 2, 4, 5], [3, 7, 9, 11], [6, 8, 10, 12]]
[[1, 2, 5, 7], [3, 6, 8, 9], [4, 10, 11, 12]]
[[1, 3, 5, 6], [2, 4, 8, 10], [7, 9, 11, 12]]
[[1, 3, 6, 8], [2, 4, 9, 10], [5, 7, 11, 12]]
[[1, 4, 6, 7], [2, 5, 9, 11], [3, 8, 10, 12]]
[[1, 2, 4, 9], [3, 5, 7, 11], [6, 8, 10, 12]]
[[1, 2, 5, 8], [3, 6, 7, 10], [4, 9, 11, 12]]
[[1, 2, 3, 5], [4, 6, 8, 10], [7, 9, 11, 12]]
[[1, 3, 6, 9], [2, 4, 8, 11], [5, 7, 10, 12]]
[[1, 3, 4, 6], [2, 7, 9, 11], [5, 8, 10, 12]]
[[1, 2, 4, 7], [3, 5, 9, 10], [6, 8, 11, 12]]
[[1, 2, 5, 7], [3, 4, 8, 10], [6, 9, 11, 12]]
[[1, 3, 5, 8], [2, 4, 6, 11], [7, 9, 10, 12]]
[[1, 3, 6, 8], [2, 5, 9, 11], [4, 7, 10, 12]]
[[1, 2, 4, 6], [3, 5, 7, 9], [8, 10, 11, 12]]
[[1, 2, 4, 9], [3, 6, 7, 10], [5, 8, 11, 12]]
[[1, 3, 5, 7], [2, 6, 8, 10], [4, 9, 11, 12]]
[[1, 3, 5, 10], [2, 4, 8, 11], [6, 7, 9, 12]]
[[1, 2, 6, 8], [3, 4, 9, 11], [5, 7, 10, 12]]
[[1, 2, 4, 6], [3, 5, 9, 11], [7, 8, 10, 12]]
[[1, 2, 3, 9], [4, 5, 7, 10], [6, 8, 11, 12]]
[[1, 3, 5, 7], [2, 4, 6, 10], [8, 9, 11, 12]]


1 3 4 9 
2 6 7 11 
5 8 10 12
124

[[1, 3, 5, 8], [2, 6, 7, 11], [4, 9, 10, 12]]
[[1, 2, 4, 5], [3, 7, 8, 10], [6, 9, 11, 12]]
[[1, 2, 4, 6], [3, 7, 8, 9], [5, 10, 11, 12]]
[[1, 3, 5, 6], [2, 4, 9, 11], [7, 8, 10, 12]]
[[1, 3, 5, 7], [2, 4, 9, 10], [6, 8, 11, 12]]
[[1, 2, 4, 7], [3, 5, 6, 10], [8, 9, 11, 12]]
[[1, 2, 4, 8], [3, 5, 6, 11], [7, 9, 10, 12]]
[[1, 2, 3, 5], [4, 6, 7, 9], [8, 10, 11, 12]]
[[1, 3, 4, 6], [2, 7, 8, 10], [5, 9, 11, 12]]
[[1, 2, 5, 7], [3, 4, 9, 11], [6, 8, 10, 12]]
[[1, 2, 3, 8], [4, 5, 6, 10], [7, 9, 11, 12]]


1 3 5 9 
2 4 8 11 
6 7 10 12
123

[[1, 3, 6, 7], [2, 5, 9, 11], [4, 8, 10, 12]]
[[1, 2, 4, 6], [3, 5, 9, 10], [7, 8, 11, 12]]
[[1, 2, 4, 8], [3, 6, 7, 10], [5, 9, 11, 12]]
[[1, 3, 5, 7], [2, 4, 6, 11], [8, 9, 10, 12]]
[[1, 2, 4, 6], [3, 5, 7, 8], [9, 10, 11, 12]]
[[1, 3, 5, 7], [2, 6, 8, 9], [4, 10, 11, 12]]
[[1, 2, 6, 8], [3, 4, 9, 10], [5, 7, 11, 12]]
[[1, 2, 3, 9], [4, 5, 7, 11], [6, 8, 10, 12]]
[[1, 2, 3, 4], [5, 6, 8, 10], [7, 9, 11, 12]]
[[1, 3, 4, 5], [2, 7, 9, 11], [6, 8, 10, 12]]
[[1, 2, 5, 6], [3, 4, 8, 10], [7, 9, 11, 12]]


1 3 5 9 
2 6 7 11 
4 8 10 12
43

[[1, 2, 4, 6], [3, 7, 8, 10], [5, 9, 11, 12]]
[[1, 3, 5, 7], [2, 4, 9, 11], [6, 8, 10, 12]]
[[1, 2, 4, 8], [3, 5, 6, 10], [7, 9, 11, 12]]


1 3 6 10 
2 4 8 11 
5 7 9 12
121

[[1, 4, 6, 8], [2, 5, 9, 11], [3, 7, 10, 12]]
[[1, 2, 4, 7], [3, 5, 9, 11], [6, 8, 10, 12]]
[[1, 2, 5, 9], [3, 6, 7, 10], [4, 8, 11, 12]]
[[1, 3, 5, 8], [2, 4, 6, 10], [7, 9, 11, 12]]
[[1, 4, 6, 9], [2, 5, 7, 11], [3, 8, 10, 12]]
[[1, 2, 5, 7], [3, 6, 8, 10], [4, 9, 11, 12]]
[[1, 3, 6, 8], [2, 4, 9, 11], [5, 7, 10, 12]]
[[1, 2, 4, 9], [3, 5, 7, 10], [6, 8, 11, 12]]
[[1, 3, 5, 10], [2, 6, 8, 11], [4, 7, 9, 12]]
[[1, 2, 4, 6], [3, 7, 9, 11], [5, 8, 10, 12]]
[[1, 3, 5, 7], [2, 4, 8, 10], [6, 9, 11, 12]]


1 3 6 10 
2 5 8 11 
4 7 9 12
122

[[1, 4, 6, 9], [2, 5, 8, 11], [3, 7, 10, 12]]
[[1, 2, 4, 7], [3, 6, 9, 11], [5, 8, 10, 12]]
[[1, 2, 5, 7], [3, 6, 9, 10], [4, 8, 11, 12]]
[[1, 3, 5, 8], [2, 4, 7, 10], [6, 9, 11, 12]]
[[1, 3, 6, 8], [2, 4, 7, 11], [5, 9, 10, 12]]
[[1, 2, 4, 7], [3, 5, 8, 9], [6, 10, 11, 12]]
[[1, 3, 5, 8], [2, 6, 9, 10], [4, 7, 11, 12]]
[[1, 2, 6, 9], [3, 4, 7, 11], [5, 8, 10, 12]]
[[1, 2, 3, 7], [4, 5, 8, 10], [6, 9, 11, 12]]
[[1, 3, 4, 8], [2, 6, 9, 11], [5, 7, 10, 12]]
[[1, 2, 5, 9], [3, 4, 7, 10], [6, 8, 11, 12]]


1 3 6 9 
2 5 8 11 
4 7 10 12
123

[[1, 2, 4, 7], [3, 6, 9, 10], [5, 8, 11, 12]]
[[1, 3, 5, 8], [2, 4, 7, 11], [6, 9, 10, 12]]
[[1, 2, 4, 6], [3, 5, 8, 9], [7, 10, 11, 12]]
[[1, 3, 5, 7], [2, 6, 9, 10], [4, 8, 11, 12]]
[[1, 2, 6, 8], [3, 4, 7, 11], [5, 9, 10, 12]]
[[1, 2, 3, 7], [4, 5, 8, 9], [6, 10, 11, 12]]
[[1, 3, 4, 8], [2, 6, 9, 10], [5, 7, 11, 12]]
[[1, 2, 5, 9], [3, 4, 7, 11], [6, 8, 10, 12]]
[[1, 2, 3, 6], [4, 5, 8, 10], [7, 9, 11, 12]]
[[1, 3, 4, 7], [2, 6, 9, 11], [5, 8, 10, 12]]
[[1, 2, 5, 8], [3, 4, 7, 10], [6, 9, 11, 12]]


1 3 7 10 
2 5 8 11 
4 6 9 12
121

[[1, 4, 7, 9], [2, 5, 8, 11], [3, 6, 10, 12]]
[[1, 2, 4, 8], [3, 6, 9, 11], [5, 7, 10, 12]]
[[1, 2, 5, 8], [3, 6, 9, 10], [4, 7, 11, 12]]
[[1, 3, 5, 9], [2, 4, 7, 10], [6, 8, 11, 12]]
[[1, 3, 6, 9], [2, 4, 7, 11], [5, 8, 10, 12]]
[[1, 4, 6, 10], [2, 5, 8, 11], [3, 7, 9, 12]]
[[1, 2, 4, 7], [3, 5, 8, 10], [6, 9, 11, 12]]
[[1, 2, 5, 7], [3, 6, 9, 11], [4, 8, 10, 12]]
[[1, 3, 5, 8], [2, 6, 9, 11], [4, 7, 10, 12]]
[[1, 3, 6, 8], [2, 4, 7, 10], [5, 9, 11, 12]]
[[1, 2, 6, 9], [3, 4, 7, 10], [5, 8, 11, 12]]


1 3 7 9 
2 5 8 11 
4 6 10 12
62

[[1, 2, 4, 8], [3, 6, 9, 10], [5, 7, 11, 12]]
[[1, 3, 5, 9], [2, 4, 7, 11], [6, 8, 10, 12]]
[[1, 2, 4, 6], [3, 5, 8, 10], [7, 9, 11, 12]]
[[1, 3, 5, 7], [2, 6, 9, 11], [4, 8, 10, 12]]
[[1, 2, 6, 8], [3, 4, 7, 10], [5, 9, 11, 12]]


1 4 7 10 
2 5 8 11 
3 6 9 12
30

[[1, 2, 5, 8], [3, 6, 9, 11], [4, 7, 10, 12]]
[[1, 3, 6, 9], [2, 4, 7, 10], [5, 8, 11, 12]]