You are given an acyclic directed graph, consisting of n nodes and k edges. Find the number of edges in its transitive closure.

Transitive closure of graph G is a graph G', consisting of all nodes of original graph G and such edges (u, v) that there is a path from node u to v in graph G.

Knuth knows how to solve the problem. And what about you?

Input

The first line contains two numbers n and k (1 ≤ n, k ≤ 50000). Then k lines follow, each containing two integers ai and bi, describing directed edge from ai to bi (1 ≤ ai, bi ≤ n). Graph doesn't contain loops, cycles and multiple edges.

Output

Print the number of edges in transitive closure.