number of vertices :  24 
number of required edges  20 
1 2 3 3 9
2 3 4 4 4
4 5 4 4 8
6 7 6 6 17
7 8 3 3 5
7 9 4 4 12
8 9 5 5 12
10 11 2 2 2
12 13 3 3 6
12 14 3 3 4
13 14 2 2 6
15 16 4 4 5
15 17 3 3 5
15 19 4 4 11
16 17 2 2 3
18 19 1 1 1
20 22 4 4 7
21 22 2 2 2
22 23 6 6 15
22 24 5 5 13
number of non required edges  26 
1 3 5 5 4
1 18 6 6 5
3 4 1 1 0
3 16 5 5 3
3 18 4 4 1
4 20 3 3 1
5 6 6 6 1
5 20 4 4 2
5 21 5 5 0
6 9 8 8 3
6 21 2 2 0
8 10 5 5 0
9 10 3 3 1
10 23 3 3 2
11 12 4 4 3
11 14 2 2 1
13 15 3 3 1
14 15 4 4 2
14 16 1 1 0
14 23 6 6 0
16 20 4 4 3
16 24 2 2 1
17 18 2 2 0
20 21 5 5 0
21 23 7 7 4
23 24 8 8 5
