You will be given a bipartite graph, each side have N nodes where N<=10^5. There will be M<=10^5 edges between these nodes. It is guranteed that the initial graph is given in such a way that the graph has exactly N matching. How many edges are there if I remove one of them the matching of the graph will be less than N? Here is the problem https://open.kattis.com/problems/justenoughbridges.

Any idea?