*Please provide solution in Python or C++*

*Must be able to pass test cases up to sizes according to the constraints*

*It is essentially a Min Vector Cover Problem but not an approximation, it uses Branch-and-Bound*

Sample Input

12 25 0 2 0 4 0 7 0 10 1 6 1 8 1 10 2 5 2 6 2 7 2 10 3 6 3 7 3 8 3 9 4 5 4 9 5 8 5 10 6 11 7 8 7 9 8 9 9 11 10 11 

Sample Output

7 

I am taking over villages that will allow me to gain control of my region. I must determine the smallest number of villages that I can control to make sure that I have a presence on at least one side of every single village. Hint: A branch-and-bound approach is needed to come up with a solution to this problem. Input Format The first line contains two values, the number of villages (N) and the number of roads linking villages (M) The next M lines each describe a road, indicating the village ID on either side. Constraints 1 s N s 200 1 s M s 10,000 0 s Village IDsN Output Format A single number indicating the minimum number of villages that can possibly be controlled to make sure that one is controlled on at least one side of every road. I am taking over villages that will allow me to gain control of my region. I must determine the smallest number of villages that I can control to make sure that I have a presence on at least one side of every single village. Hint: A branch-and-bound approach is needed to come up with a solution to this problem. Input Format The first line contains two values, the number of villages (N) and the number of roads linking villages (M) The next M lines each describe a road, indicating the village ID on either side. Constraints 1 s N s 200 1 s M s 10,000 0 s Village IDsN Output Format A single number indicating the minimum number of villages that can possibly be controlled to make sure that one is controlled on at least one side of every road