Covering with paths

Input

The first line of input contains the number of vertices $n$ and the number of edges $m$ (2 \leq n \leq 1000, 0 \leq m \leq 10^5). Each of the next $m$ lines contains two numbers: the numbers of the vertices $u$ and $v$ connected by a directed edge ($u$, $v$).

Output

In the first line of output print a natural number $k$ representing the minimum number of paths needed to cover all the vertices.

Examples