number of vertices :  23 
number of required edges  16 
1 2 0 0 0
3 4 4 4 4
4 5 2 2 4
5 6 3 3 9
5 7 5 5 8
8 9 3 3 9
10 11 2 2 5
10 12 1 1 1
11 12 2 2 4
12 13 2 2 3
14 15 1 1 3
16 17 13 13 18
17 18 12 12 21
18 19 7 7 18
20 21 1 1 1
22 23 3 3 4
number of non required edges  21 
1 23 3 3 1
2 7 13 13 1
2 19 11 11 7
2 22 3 3 2
3 7 1 1 0
4 8 28 28 25
4 12 24 24 12
6 18 1 1 0
7 19 4 4 1
7 22 12 12 5
8 16 21 21 6
9 10 3 3 1
11 14 9 9 0
12 16 17 17 8
12 17 13 13 2
13 15 7 7 0
16 18 6 6 3
17 19 3 3 2
17 20 6 6 5
19 22 10 10 9
21 22 4 4 2
