Detecting Circular Dependencies

In modern file systems, folders may be related by subfolder relationships or symbolic links, which can sometimes lead to circular dependencies. In this problem, you are given a directed graph with $n$ nodes and $m$ edges. Each node represents a folder, and each directed edge $(u, v)$ represents a relationship from folder $u$ to folder $v$. Your task is to determine whether the graph contains a cycle, i.e. a circular dependency.

Constraints:

• $1 \le n \le 10^5$
• $0 \le m \le 10^5$

If there is at least one cycle in the graph, output YES; otherwise, output NO.

inputFormat

The input is read from standard input (stdin) and has the following format:

• The first line contains two space-separated integers $n$ and $m$, representing the number of folders and the number of relationships respectively.
• Each of the following $m$ lines contains two space-separated integers $u$ and $v$, indicating there is an edge from folder $u$ to folder $v$.

outputFormat

Print a single line to standard output (stdout) containing YES if there is a cycle (circular dependency) in the graph, and NO otherwise.## sample

5 6
1 2
2 3
3 4
4 5
5 2
3 1

YES