Is it cyclic? P45234

Write a program that, given a directed graph, determines whether the graph has any cycle or not.

Input

Input consists of several cases. Every case begins with the number of vertices n and the number of arcs m of a graph G. Follow m pairs u, v, indicating that there is an arc u → v in G, with u ≠ v. Assume 1 ≤ n ≤ 10⁴, 0 ≤ m ≤ 5n, and that for every pair of vertices u and v there is at most one arc of the kind u → v. Vertices are numbered from 0 to n−1.

Output

For every case, print “yes” or “no” depending on whether the graph has any cycle or not.