Strong connectivity

A strongly connected component in a directed graph is a set of vertices such that there is a path from any vertex to any other vertex in the set. Moreover, there is no larger set with this property containing this set.

Given a directed graph. Find the number of strongly connected components.

Input

The first line contains two integers $n$ and $m(1\le n\le 10,0\le m\le 90)$ — the number of vertices and edges in the graph, respectively. The next $m$ lines describe the edges: the $i$-th line contains two integers $u_i$ and $v_i(1\le u_i,v_i\le n)$ — the start and the end of the $i$-th edge respectively. It is guaranteed that the graph has no loops or multiple edges.

Output

Print the number of strongly connected components in the graph.

Examples