Is it cyclic? X64801

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 $m$. Follow $m$ pairs $u$, $v$, indicating that there is an arc $u \rightarrow v$, where $u \neq v$. Assume $1 \leq n \leq 10^{4}$, $0 \leq m \leq 5n$, and that for every pair of vertices $u$ and $v$ there is at most one arc of the kind $u \rightarrow v$. 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.