number of vertices :  14 
number of required edges  14 
1 2 2 2 6
2 3 3 3 3
2 4 5 5 10
3 4 1 1 3
4 5 7 7 12
6 9 5 5 15
6 11 9 9 21
7 8 2 2 2
7 9 1 1 2
8 9 3 3 4
9 10 3 3 9
9 11 4 4 5
12 13 3 3 5
13 14 9 9 24
number of non required edges  12 
1 4 3 3 0
3 5 4 4 1
5 6 4 4 1
5 11 6 6 0
5 13 9 9 6
5 14 4 4 2
8 10 3 3 2
10 11 1 1 0
10 12 6 6 3
10 14 8 8 6
11 13 4 4 1
12 14 7 7 3
 