a,b,c,d,e,f,g
0,0,0,0,a,2,c
1,1,1,0,b,4,d
2,2,0,0,c,6,e
3,3,1,0,d,8,cde
4,4,0,0,abc,10,a
5,0,1,0,cde,12,b
6,1,0,0,a,14,c
7,2,1,0,b,16,abc
8,3,0,0,c,18,c
9,4,1,0,d,20,d
10,0,0,0,abc,22,e
11,1,1,0,cde,24,cde
12,2,0,0,a,26,a
13,3,1,0,b,28,b
14,4,0,0,c,30,c
15,0,1,0,d,32,abc
16,1,0,0,abc,34,c
17,2,1,0,cde,36,d
18,3,0,0,a,38,e
19,4,1,0,b,40,cde