Covering with paths

An oriented acyclic graph is given. Find the minimum number of disjoint paths covering all vertices.

Input

First line contains number of vertices n and number of edges m (2 ≤ n ≤ 1000, 0 ≤ m ≤ 10^5). Each of the next m lines contains two numbers: the numbers of the vertces u and v connected with an edge (u, v).

Output

Print the minimum number of paths that can cover all the vertices.

Examples