General graph matching

A graph with $N$ vertices and $M$ undirected edges is given. Write a program that prints the size of a maximum matching of that graph.

In a graph $G = (V, E)$ ($|V| = N$, $|E| = M$), a matching $T$ is a subset of $E$ in which no two elements share a vertex.

A maximum matching is a matching of the largest possible size.

The first line contains the number of vertices $N$ ($1 \le N \le 500$) and the number of edges $M$ ($1 \le M \le 124750$).

Each of the next $M$ lines describes one edge.

An edge is described by the numbers of the two distinct vertices it joins.

Every vertex number is a natural number between $1$ and $N$.

At most one edge joins any given pair of vertices.

Print the size of a maximum matching on the first line.