E8

# Dynkin diagram
 
           2
           |
   1---3---4---5---6---7---8
 
# coordinates (and numbering of) the positive co-roots

1   [1, 0, 0, 0, 0, 0, 0, 0]
2   [0, 1, 0, 0, 0, 0, 0, 0]
3   [0, 0, 1, 0, 0, 0, 0, 0]
4   [0, 0, 0, 1, 0, 0, 0, 0]
5   [0, 0, 0, 0, 1, 0, 0, 0]
6   [0, 0, 0, 0, 0, 1, 0, 0]
7   [0, 0, 0, 0, 0, 0, 1, 0]
8   [0, 0, 0, 0, 0, 0, 0, 1]
9   [1, 0, 1, 0, 0, 0, 0, 0]
10   [0, 1, 0, 1, 0, 0, 0, 0]
11   [0, 0, 1, 1, 0, 0, 0, 0]
12   [0, 0, 0, 1, 1, 0, 0, 0]
13   [0, 0, 0, 0, 1, 1, 0, 0]
14   [0, 0, 0, 0, 0, 1, 1, 0]
15   [0, 0, 0, 0, 0, 0, 1, 1]
16   [1, 0, 1, 1, 0, 0, 0, 0]
17   [0, 1, 1, 1, 0, 0, 0, 0]
18   [0, 1, 0, 1, 1, 0, 0, 0]
19   [0, 0, 1, 1, 1, 0, 0, 0]
20   [0, 0, 0, 1, 1, 1, 0, 0]
21   [0, 0, 0, 0, 1, 1, 1, 0]
22   [0, 0, 0, 0, 0, 1, 1, 1]
23   [1, 1, 1, 1, 0, 0, 0, 0]
24   [1, 0, 1, 1, 1, 0, 0, 0]
25   [0, 1, 1, 1, 1, 0, 0, 0]
26   [0, 1, 0, 1, 1, 1, 0, 0]
27   [0, 0, 1, 1, 1, 1, 0, 0]
28   [0, 0, 0, 1, 1, 1, 1, 0]
29   [0, 0, 0, 0, 1, 1, 1, 1]
30   [1, 1, 1, 1, 1, 0, 0, 0]
31   [1, 0, 1, 1, 1, 1, 0, 0]
32   [0, 1, 1, 2, 1, 0, 0, 0]
33   [0, 1, 1, 1, 1, 1, 0, 0]
34   [0, 1, 0, 1, 1, 1, 1, 0]
35   [0, 0, 1, 1, 1, 1, 1, 0]
36   [0, 0, 0, 1, 1, 1, 1, 1]
37   [1, 1, 1, 2, 1, 0, 0, 0]
38   [1, 1, 1, 1, 1, 1, 0, 0]
39   [1, 0, 1, 1, 1, 1, 1, 0]
40   [0, 1, 1, 2, 1, 1, 0, 0]
41   [0, 1, 1, 1, 1, 1, 1, 0]
42   [0, 1, 0, 1, 1, 1, 1, 1]
43   [0, 0, 1, 1, 1, 1, 1, 1]
44   [1, 1, 2, 2, 1, 0, 0, 0]
45   [1, 1, 1, 2, 1, 1, 0, 0]
46   [1, 1, 1, 1, 1, 1, 1, 0]
47   [1, 0, 1, 1, 1, 1, 1, 1]
48   [0, 1, 1, 2, 2, 1, 0, 0]
49   [0, 1, 1, 2, 1, 1, 1, 0]
50   [0, 1, 1, 1, 1, 1, 1, 1]
51   [1, 1, 2, 2, 1, 1, 0, 0]
52   [1, 1, 1, 2, 2, 1, 0, 0]
53   [1, 1, 1, 2, 1, 1, 1, 0]
54   [1, 1, 1, 1, 1, 1, 1, 1]
55   [0, 1, 1, 2, 2, 1, 1, 0]
56   [0, 1, 1, 2, 1, 1, 1, 1]
57   [1, 1, 2, 2, 2, 1, 0, 0]
58   [1, 1, 2, 2, 1, 1, 1, 0]
59   [1, 1, 1, 2, 2, 1, 1, 0]
60   [1, 1, 1, 2, 1, 1, 1, 1]
61   [0, 1, 1, 2, 2, 2, 1, 0]
62   [0, 1, 1, 2, 2, 1, 1, 1]
63   [1, 1, 2, 3, 2, 1, 0, 0]
64   [1, 1, 2, 2, 2, 1, 1, 0]
65   [1, 1, 2, 2, 1, 1, 1, 1]
66   [1, 1, 1, 2, 2, 2, 1, 0]
67   [1, 1, 1, 2, 2, 1, 1, 1]
68   [0, 1, 1, 2, 2, 2, 1, 1]
69   [1, 2, 2, 3, 2, 1, 0, 0]
70   [1, 1, 2, 3, 2, 1, 1, 0]
71   [1, 1, 2, 2, 2, 2, 1, 0]
72   [1, 1, 2, 2, 2, 1, 1, 1]
73   [1, 1, 1, 2, 2, 2, 1, 1]
74   [0, 1, 1, 2, 2, 2, 2, 1]
75   [1, 2, 2, 3, 2, 1, 1, 0]
76   [1, 1, 2, 3, 2, 2, 1, 0]
77   [1, 1, 2, 3, 2, 1, 1, 1]
78   [1, 1, 2, 2, 2, 2, 1, 1]
79   [1, 1, 1, 2, 2, 2, 2, 1]
80   [1, 2, 2, 3, 2, 2, 1, 0]
81   [1, 2, 2, 3, 2, 1, 1, 1]
82   [1, 1, 2, 3, 3, 2, 1, 0]
83   [1, 1, 2, 3, 2, 2, 1, 1]
84   [1, 1, 2, 2, 2, 2, 2, 1]
85   [1, 2, 2, 3, 3, 2, 1, 0]
86   [1, 2, 2, 3, 2, 2, 1, 1]
87   [1, 1, 2, 3, 3, 2, 1, 1]
88   [1, 1, 2, 3, 2, 2, 2, 1]
89   [1, 2, 2, 4, 3, 2, 1, 0]
90   [1, 2, 2, 3, 3, 2, 1, 1]
91   [1, 2, 2, 3, 2, 2, 2, 1]
92   [1, 1, 2, 3, 3, 2, 2, 1]
93   [1, 2, 3, 4, 3, 2, 1, 0]
94   [1, 2, 2, 4, 3, 2, 1, 1]
95   [1, 2, 2, 3, 3, 2, 2, 1]
96   [1, 1, 2, 3, 3, 3, 2, 1]
97   [2, 2, 3, 4, 3, 2, 1, 0]
98   [1, 2, 3, 4, 3, 2, 1, 1]
99   [1, 2, 2, 4, 3, 2, 2, 1]
100   [1, 2, 2, 3, 3, 3, 2, 1]
101   [2, 2, 3, 4, 3, 2, 1, 1]
102   [1, 2, 3, 4, 3, 2, 2, 1]
103   [1, 2, 2, 4, 3, 3, 2, 1]
104   [2, 2, 3, 4, 3, 2, 2, 1]
105   [1, 2, 3, 4, 3, 3, 2, 1]
106   [1, 2, 2, 4, 4, 3, 2, 1]
107   [2, 2, 3, 4, 3, 3, 2, 1]
108   [1, 2, 3, 4, 4, 3, 2, 1]
109   [2, 2, 3, 4, 4, 3, 2, 1]
110   [1, 2, 3, 5, 4, 3, 2, 1]
111   [2, 2, 3, 5, 4, 3, 2, 1]
112   [1, 3, 3, 5, 4, 3, 2, 1]
113   [2, 3, 3, 5, 4, 3, 2, 1]
114   [2, 2, 4, 5, 4, 3, 2, 1]
115   [2, 3, 4, 5, 4, 3, 2, 1]
116   [2, 3, 4, 6, 4, 3, 2, 1]
117   [2, 3, 4, 6, 5, 3, 2, 1]
118   [2, 3, 4, 6, 5, 4, 2, 1]
119   [2, 3, 4, 6, 5, 4, 3, 1]
120   [2, 3, 4, 6, 5, 4, 3, 2]

# f-vector of the cell complex, first segregated by faces of the
# dominant chamber, and then cumulative (q marks co-dimension):

[0, 0, 0, 0, 0, 0, 0, 0, 0]   {1, 2, 3, 4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 2]   {2, 3, 4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 3]   {1, 3, 4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 9, 2]   {3, 4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 2]   {1, 2, 4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 7, 1]   {2, 4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 4, 1]   {1, 4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 22, 10, 1]   {4, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 1]   {1, 2, 3, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 2, 1]   {2, 3, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 5, 1]   {1, 3, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 9, 7, 1]   {3, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 1, 1]   {1, 2, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 11, 9, 1]   {2, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 6, 5, 1]   {1, 5, 6, 7, 8}
[0, 0, 0, 0, 0, 54, 45, 12, 1]   {5, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 3]   {1, 2, 3, 4, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 6, 4]   {2, 3, 4, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 5, 1]   {1, 3, 4, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 14, 14, 2]   {3, 4, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 1, 1]   {1, 2, 4, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 12, 10, 1]   {2, 4, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 1, 5, 1]   {1, 4, 6, 7, 8}
[0, 0, 0, 0, 0, 24, 45, 19, 2]   {4, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 1, 1]   {1, 2, 3, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 3, 4, 1]   {2, 3, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 7, 5, 1]   {1, 3, 6, 7, 8}
[0, 0, 0, 0, 0, 20, 36, 13, 1]   {3, 6, 7, 8}
[0, 0, 0, 0, 0, 0, 1, 3, 1]   {1, 2, 6, 7, 8}
[0, 0, 0, 0, 0, 18, 28, 10, 1]   {2, 6, 7, 8}
[0, 0, 0, 0, 0, 12, 28, 12, 1]   {1, 6, 7, 8}
[0, 0, 0, 0, 191, 264, 127, 23, 1]   {6, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 2]   {1, 2, 3, 4, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 5, 4]   {2, 3, 4, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 7, 3]   {1, 3, 4, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 16, 21, 3]   {3, 4, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 2, 4]   {1, 2, 4, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 18, 19, 2]   {2, 4, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 2, 12, 2]   {1, 4, 5, 7, 8}
[0, 0, 0, 0, 0, 34, 84, 32, 3]   {4, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 1]   {1, 2, 3, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 4, 3]   {2, 3, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 1, 5, 1]   {1, 3, 5, 7, 8}
[0, 0, 0, 0, 0, 2, 36, 21, 2]   {3, 5, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 2, 1]   {1, 2, 5, 7, 8}
[0, 0, 0, 0, 0, 1, 22, 14, 1]   {2, 5, 7, 8}
[0, 0, 0, 0, 0, 2, 23, 11, 1]   {1, 5, 7, 8}
[0, 0, 0, 0, 74, 221, 140, 26, 1]   {5, 7, 8}
[0, 0, 0, 0, 0, 0, 0, 4, 1]   {1, 2, 3, 4, 7, 8}
[0, 0, 0, 0, 0, 0, 10, 16, 1]   {2, 3, 4, 7, 8}
[0, 0, 0, 0, 0, 0, 9, 9, 1]   {1, 3, 4, 7, 8}
[0, 0, 0, 0, 0, 32, 73, 28, 3]   {3, 4, 7, 8}
[0, 0, 0, 0, 0, 0, 2, 8, 1]   {1, 2, 4, 7, 8}
[0, 0, 0, 0, 0, 26, 48, 14, 1]   {2, 4, 7, 8}
[0, 0, 0, 0, 0, 2, 28, 17, 2]   {1, 4, 7, 8}
[0, 0, 0, 0, 80, 273, 208, 58, 5]   {4, 7, 8}
[0, 0, 0, 0, 0, 0, 2, 8, 1]   {1, 2, 3, 7, 8}
[0, 0, 0, 0, 0, 9, 29, 15, 1]   {2, 3, 7, 8}
[0, 0, 0, 0, 0, 15, 30, 10, 1]   {1, 3, 7, 8}
[0, 0, 0, 0, 62, 206, 132, 26, 1]   {3, 7, 8}
[0, 0, 0, 0, 0, 3, 15, 8, 1]   {1, 2, 7, 8}
[0, 0, 0, 0, 52, 145, 86, 16, 1]   {2, 7, 8}
[0, 0, 0, 0, 33, 130, 92, 21, 1]   {1, 7, 8}
[0, 0, 0, 812, 1551, 1091, 336, 40, 1]   {7, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 1]   {1, 2, 3, 4, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 4, 3]   {2, 3, 4, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 7, 4]   {1, 3, 4, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 20, 26, 5]   {3, 4, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 2, 4]   {1, 2, 4, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 17, 18, 2]   {2, 4, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 3, 18, 4]   {1, 4, 5, 6, 8}
[0, 0, 0, 0, 0, 42, 105, 39, 3]   {4, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 0, 5]   {1, 2, 3, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 15, 6]   {2, 3, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 3, 14, 2]   {1, 3, 5, 6, 8}
[0, 0, 0, 0, 0, 6, 67, 31, 2]   {3, 5, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 8, 2]   {1, 2, 5, 6, 8}
[0, 0, 0, 0, 0, 4, 55, 24, 1]   {2, 5, 6, 8}
[0, 0, 0, 0, 0, 4, 41, 16, 1]   {1, 5, 6, 8}
[0, 0, 0, 0, 101, 337, 184, 28, 1]   {5, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 1, 2]   {1, 2, 3, 4, 6, 8}
[0, 0, 0, 0, 0, 0, 2, 18, 5]   {2, 3, 4, 6, 8}
[0, 0, 0, 0, 0, 0, 2, 12, 3]   {1, 3, 4, 6, 8}
[0, 0, 0, 0, 0, 4, 72, 46, 6]   {3, 4, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 10, 4]   {1, 2, 4, 6, 8}
[0, 0, 0, 0, 0, 3, 57, 35, 4]   {2, 4, 6, 8}
[0, 0, 0, 0, 0, 0, 23, 20, 2]   {1, 4, 6, 8}
[0, 0, 0, 0, 6, 219, 227, 66, 5]   {4, 6, 8}
[0, 0, 0, 0, 0, 0, 0, 8, 1]   {1, 2, 3, 6, 8}
[0, 0, 0, 0, 0, 0, 29, 22, 2]   {2, 3, 6, 8}
[0, 0, 0, 0, 0, 3, 30, 12, 1]   {1, 3, 6, 8}
[0, 0, 0, 0, 6, 174, 152, 31, 1]   {3, 6, 8}
[0, 0, 0, 0, 0, 0, 14, 11, 1]   {1, 2, 6, 8}
[0, 0, 0, 0, 4, 133, 111, 21, 1]   {2, 6, 8}
[0, 0, 0, 0, 9, 99, 94, 21, 1]   {1, 6, 8}
[0, 0, 0, 288, 1150, 1065, 347, 40, 1]   {6, 8}
[0, 0, 0, 0, 0, 0, 0, 2, 1]   {1, 2, 3, 4, 5, 8}
[0, 0, 0, 0, 0, 0, 8, 14, 1]   {2, 3, 4, 5, 8}
[0, 0, 0, 0, 0, 0, 12, 14, 1]   {1, 3, 4, 5, 8}
[0, 0, 0, 0, 0, 42, 102, 39, 3]   {3, 4, 5, 8}
[0, 0, 0, 0, 0, 0, 3, 15, 3]   {1, 2, 4, 5, 8}
[0, 0, 0, 0, 0, 38, 77, 26, 1]   {2, 4, 5, 8}
[0, 0, 0, 0, 0, 4, 62, 40, 5]   {1, 4, 5, 8}
[0, 0, 0, 0, 122, 480, 366, 94, 7]   {4, 5, 8}
[0, 0, 0, 0, 0, 0, 0, 9, 2]   {1, 2, 3, 5, 8}
[0, 0, 0, 0, 0, 0, 32, 32, 7]   {2, 3, 5, 8}
[0, 0, 0, 0, 0, 3, 34, 15, 1]   {1, 3, 5, 8}
[0, 0, 0, 0, 9, 186, 206, 67, 5]   {3, 5, 8}
[0, 0, 0, 0, 0, 0, 17, 14, 1]   {1, 2, 5, 8}
[0, 0, 0, 0, 4, 158, 152, 37, 1]   {2, 5, 8}
[0, 0, 0, 0, 5, 110, 102, 23, 1]   {1, 5, 8}
[0, 0, 0, 296, 1305, 1347, 524, 73, 2]   {5, 8}
[0, 0, 0, 0, 0, 0, 6, 9, 1]   {1, 2, 3, 4, 8}
[0, 0, 0, 0, 0, 26, 76, 24, 1]   {2, 3, 4, 8}
[0, 0, 0, 0, 0, 21, 55, 17, 1]   {1, 3, 4, 8}
[0, 0, 0, 0, 107, 393, 272, 63, 4]   {3, 4, 8}
[0, 0, 0, 0, 0, 7, 43, 20, 1]   {1, 2, 4, 8}
[0, 0, 0, 0, 94, 302, 180, 31, 1]   {2, 4, 8}
[0, 0, 0, 0, 8, 121, 129, 37, 3]   {1, 4, 8}
[0, 0, 0, 304, 1471, 1635, 732, 140, 9]   {4, 8}
[0, 0, 0, 0, 0, 5, 35, 13, 1]   {1, 2, 3, 8}
[0, 0, 0, 0, 30, 149, 139, 35, 1]   {2, 3, 8}
[0, 0, 0, 0, 41, 157, 86, 16, 1]   {1, 3, 8}
[0, 0, 0, 233, 1122, 1127, 412, 51, 1]   {3, 8}
[0, 0, 0, 0, 11, 77, 68, 14, 1]   {1, 2, 8}
[0, 0, 0, 205, 850, 761, 234, 24, 1]   {2, 8}
[0, 0, 0, 107, 654, 660, 236, 32, 1]   {1, 8}
[0, 0, 3941, 9726, 9097, 4027, 838, 68, 1]   {8}
[0, 0, 0, 0, 0, 0, 0, 0, 1]   {1, 2, 3, 4, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 0, 8, 3]   {2, 3, 4, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 0, 12, 3]   {1, 3, 4, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 45, 29, 4]   {3, 4, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 0, 6, 5]   {1, 2, 4, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 36, 21, 1]   {2, 4, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 15, 21, 4]   {1, 4, 5, 6, 7}
[0, 0, 0, 0, 0, 134, 135, 39, 3]   {4, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 0, 2, 5]   {1, 2, 3, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 4, 15, 5]   {2, 3, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 16, 19, 1]   {1, 3, 5, 6, 7}
[0, 0, 0, 0, 0, 35, 87, 32, 2]   {3, 5, 6, 7}
[0, 0, 0, 0, 0, 0, 3, 10, 1]   {1, 2, 5, 6, 7}
[0, 0, 0, 0, 0, 41, 75, 24, 1]   {2, 5, 6, 7}
[0, 0, 0, 0, 0, 30, 58, 17, 1]   {1, 5, 6, 7}
[0, 0, 0, 0, 377, 504, 210, 30, 1]   {5, 6, 7}
[0, 0, 0, 0, 0, 0, 0, 8, 5]   {1, 2, 3, 4, 6, 7}
[0, 0, 0, 0, 0, 0, 22, 40, 8]   {2, 3, 4, 6, 7}
[0, 0, 0, 0, 0, 0, 17, 25, 5]   {1, 3, 4, 6, 7}
[0, 0, 0, 0, 0, 59, 155, 73, 9]   {3, 4, 6, 7}
[0, 0, 0, 0, 0, 0, 3, 19, 5]   {1, 2, 4, 6, 7}
[0, 0, 0, 0, 0, 46, 115, 40, 2]   {2, 4, 6, 7}
[0, 0, 0, 0, 0, 6, 45, 24, 2]   {1, 4, 6, 7}
[0, 0, 0, 0, 118, 433, 309, 73, 5]   {4, 6, 7}
[0, 0, 0, 0, 0, 0, 3, 14, 1]   {1, 2, 3, 6, 7}
[0, 0, 0, 0, 0, 9, 50, 27, 2]   {2, 3, 6, 7}
[0, 0, 0, 0, 0, 32, 60, 16, 1]   {1, 3, 6, 7}
[0, 0, 0, 0, 107, 349, 213, 36, 1]   {3, 6, 7}
[0, 0, 0, 0, 0, 4, 31, 13, 1]   {1, 2, 6, 7}
[0, 0, 0, 0, 87, 273, 147, 21, 1]   {2, 6, 7}
[0, 0, 0, 0, 81, 238, 138, 25, 1]   {1, 6, 7}
[0, 0, 0, 1386, 2515, 1585, 417, 42, 1]   {6, 7}
[0, 0, 0, 0, 0, 0, 0, 3, 2]   {1, 2, 3, 4, 5, 7}
[0, 0, 0, 0, 0, 0, 13, 24, 6]   {2, 3, 4, 5, 7}
[0, 0, 0, 0, 0, 0, 14, 25, 5]   {1, 3, 4, 5, 7}
[0, 0, 0, 0, 0, 52, 169, 88, 11]   {3, 4, 5, 7}
[0, 0, 0, 0, 0, 0, 6, 25, 8]   {1, 2, 4, 5, 7}
[0, 0, 0, 0, 0, 65, 136, 63, 6]   {2, 4, 5, 7}
[0, 0, 0, 0, 0, 12, 97, 64, 8]   {1, 4, 5, 7}
[0, 0, 0, 0, 183, 751, 582, 148, 11]   {4, 5, 7}
[0, 0, 0, 0, 0, 0, 0, 12, 5]   {1, 2, 3, 5, 7}
[0, 0, 0, 0, 0, 0, 42, 51, 12]   {2, 3, 5, 7}
[0, 0, 0, 0, 0, 5, 45, 29, 2]   {1, 3, 5, 7}
[0, 0, 0, 0, 25, 260, 294, 91, 6]   {3, 5, 7}
[0, 0, 0, 0, 0, 0, 24, 23, 2]   {1, 2, 5, 7}
[0, 0, 0, 0, 4, 229, 234, 58, 2]   {2, 5, 7}
[0, 0, 0, 0, 16, 163, 152, 30, 1]   {1, 5, 7}
[0, 0, 0, 376, 1829, 1865, 666, 82, 2]   {5, 7}
[0, 0, 0, 0, 0, 0, 10, 12, 1]   {1, 2, 3, 4, 7}
[0, 0, 0, 0, 0, 45, 120, 44, 2]   {2, 3, 4, 7}
[0, 0, 0, 0, 0, 32, 84, 32, 2]   {1, 3, 4, 7}
[0, 0, 0, 0, 151, 585, 422, 93, 4]   {3, 4, 7}
[0, 0, 0, 0, 0, 8, 68, 36, 2]   {1, 2, 4, 7}
[0, 0, 0, 0, 141, 468, 315, 66, 4]   {2, 4, 7}
[0, 0, 0, 0, 14, 191, 193, 48, 3]   {1, 4, 7}
[0, 0, 0, 428, 2102, 2267, 937, 159, 9]   {4, 7}
[0, 0, 0, 0, 0, 8, 57, 23, 1]   {1, 2, 3, 7}
[0, 0, 0, 0, 36, 237, 228, 53, 1]   {2, 3, 7}
[0, 0, 0, 0, 74, 249, 140, 21, 1]   {1, 3, 7}
[0, 0, 0, 353, 1663, 1599, 526, 55, 1]   {3, 7}
[0, 0, 0, 0, 15, 129, 108, 19, 1]   {1, 2, 7}
[0, 0, 0, 349, 1317, 1150, 339, 33, 1]   {2, 7}
[0, 0, 0, 224, 1013, 920, 286, 33, 1]   {1, 7}
[0, 0, 5579, 13482, 12058, 4933, 928, 69, 1]   {7}
[0, 0, 0, 0, 0, 0, 0, 4, 1]   {1, 2, 3, 4, 5, 6}
[0, 0, 0, 0, 0, 0, 26, 18, 2]   {2, 3, 4, 5, 6}
[0, 0, 0, 0, 0, 0, 39, 26, 4]   {1, 3, 4, 5, 6}
[0, 0, 0, 0, 0, 180, 206, 71, 7]   {3, 4, 5, 6}
[0, 0, 0, 0, 0, 0, 16, 24, 4]   {1, 2, 4, 5, 6}
[0, 0, 0, 0, 0, 134, 126, 30, 1]   {2, 4, 5, 6}
[0, 0, 0, 0, 0, 59, 142, 70, 9]   {1, 4, 5, 6}
[0, 0, 0, 0, 672, 1079, 592, 126, 8]   {4, 5, 6}
[0, 0, 0, 0, 0, 0, 5, 28, 8]   {1, 2, 3, 5, 6}
[0, 0, 0, 0, 0, 10, 106, 76, 11]   {2, 3, 5, 6}
[0, 0, 0, 0, 0, 56, 111, 38, 1]   {1, 3, 5, 6}
[0, 0, 0, 0, 179, 635, 476, 116, 7]   {3, 5, 6}
[0, 0, 0, 0, 0, 9, 64, 33, 1]   {1, 2, 5, 6}
[0, 0, 0, 0, 130, 521, 322, 52, 1]   {2, 5, 6}
[0, 0, 0, 0, 137, 383, 235, 39, 1]   {1, 5, 6}
[0, 0, 0, 2100, 4149, 2901, 850, 93, 2]   {5, 6}
[0, 0, 0, 0, 0, 0, 12, 16, 3]   {1, 2, 3, 4, 6}
[0, 0, 0, 0, 0, 52, 149, 72, 9]   {2, 3, 4, 6}
[0, 0, 0, 0, 0, 37, 90, 38, 2]   {1, 3, 4, 6}
[0, 0, 0, 0, 197, 726, 602, 174, 15]   {3, 4, 6}
[0, 0, 0, 0, 0, 9, 77, 59, 10]   {1, 2, 4, 6}
[0, 0, 0, 0, 124, 573, 476, 124, 7]   {2, 4, 6}
[0, 0, 0, 0, 26, 205, 236, 76, 6]   {1, 4, 6}
[0, 0, 0, 488, 2529, 3022, 1422, 276, 17]   {4, 6}
[0, 0, 0, 0, 0, 9, 53, 24, 1]   {1, 2, 3, 6}
[0, 0, 0, 0, 27, 248, 294, 96, 7]   {2, 3, 6}
[0, 0, 0, 0, 94, 262, 151, 23, 1]   {1, 3, 6}
[0, 0, 0, 461, 2021, 2105, 804, 105, 2]   {3, 6}
[0, 0, 0, 0, 14, 143, 144, 34, 1]   {1, 2, 6}
[0, 0, 0, 279, 1547, 1635, 604, 74, 2]   {2, 6}
[0, 0, 0, 306, 1245, 1168, 383, 42, 1]   {1, 6}
[0, 0, 6723, 16932, 16044, 7044, 1406, 102, 1]   {6}
[0, 0, 0, 0, 0, 0, 17, 10, 1]   {1, 2, 3, 4, 5}
[0, 0, 0, 0, 0, 105, 112, 28, 1]   {2, 3, 4, 5}
[0, 0, 0, 0, 0, 119, 120, 30, 1]   {1, 3, 4, 5}
[0, 0, 0, 0, 689, 1091, 570, 108, 5]   {3, 4, 5}
[0, 0, 0, 0, 0, 55, 123, 47, 4]   {1, 2, 4, 5}
[0, 0, 0, 0, 539, 785, 355, 51, 1]   {2, 4, 5}
[0, 0, 0, 0, 210, 630, 477, 124, 10]   {1, 4, 5}
[0, 0, 0, 2843, 6171, 4962, 1809, 289, 15]   {4, 5}
[0, 0, 0, 0, 0, 14, 61, 33, 3]   {1, 2, 3, 5}
[0, 0, 0, 0, 28, 286, 379, 141, 13]   {2, 3, 5}
[0, 0, 0, 0, 112, 309, 189, 31, 1]   {1, 3, 5}
[0, 0, 0, 427, 2262, 2694, 1219, 215, 11]   {3, 5}
[0, 0, 0, 0, 28, 162, 168, 41, 1]   {1, 2, 5}
[0, 0, 0, 351, 1833, 1976, 736, 87, 1]   {2, 5}
[0, 0, 0, 372, 1358, 1284, 442, 52, 1]   {1, 5}
[0, 0, 7515, 19655, 19799, 9620, 2295, 238, 7]   {5}
[0, 0, 0, 0, 0, 82, 74, 18, 1]   {1, 2, 3, 4}
[0, 0, 0, 0, 517, 766, 344, 49, 1]   {2, 3, 4}
[0, 0, 0, 0, 364, 499, 206, 25, 1]   {1, 3, 4}
[0, 0, 0, 2391, 4889, 3594, 1141, 145, 5]   {3, 4}
[0, 0, 0, 0, 161, 434, 275, 51, 1]   {1, 2, 4}
[0, 0, 0, 1949, 3874, 2755, 831, 93, 2]   {2, 4}
[0, 0, 0, 411, 1552, 1572, 604, 88, 4]   {1, 4}
[0, 0, 8208, 22016, 23007, 11813, 3075, 371, 15]   {4}
[0, 0, 0, 0, 141, 331, 165, 24, 1]   {1, 2, 3}
[0, 0, 0, 565, 1927, 1919, 711, 86, 1]   {2, 3}
[0, 0, 0, 1059, 1805, 1045, 248, 26, 1]   {1, 3}
[0, 0, 6707, 16875, 15981, 7018, 1404, 103, 1]   {3}
[0, 0, 0, 317, 1039, 881, 256, 24, 1]   {1, 2}
[0, 0, 5469, 13153, 11706, 4710, 830, 52, 1]   {2}
[0, 0, 4270, 9913, 8476, 3315, 605, 47, 1]   {1}
[25080, 100320, 163856, 140448, 67488, 17936, 2408, 128, 1]   {}
                             2           3           4           5          6
  25080 + 100320 q + 212268 q  + 281880 q  + 247266 q  + 142481 q  + 50842 q

               7        8
       + 9840 q  + 739 q