Number of paths

Input

The first line provides two integers: the number of vertices $n$ and the number of edges $k$. The constraints are 1 \le n \le 500 and 0 \le k \le n \cdot (n - 1) / 2. The next $k$ lines each contain two integers, $a$ and $b$ (where 1 \le a, b \le n), representing a directed edge from vertex $a$ to vertex $b$. Each edge $(a,b)$ is unique and appears only once.

Output

Print the minimum number of paths required.

Examples