Directed Cycle Detection

You are given a directed graph with $n$ vertices and $m$ edges. Each edge goes from one vertex to another, and vertices are numbered from $1$ to $n$.

Determine whether the graph contains at least one directed cycle. A directed cycle is a sequence of one or more edges that starts and ends at the same vertex while following edge directions.

Input

The first line contains two integers $n$ and $m$: the number of vertices and directed edges.

The next $m$ lines each contain two integers $a$ and $b$, meaning there is a directed edge from vertex $a$ to vertex $b$.

Output

Print YES if the graph contains at least one directed cycle. Otherwise, print NO.

Constraints

• $1 \le n \le 200000$
• $0 \le m \le 300000$
• $1 \le a, b \le n$

Example 1

4 3
1 2
2 3
3 4

NO

Explanation

All edges move forward along the chain, so it is impossible to return to a previous vertex.

Example 2

4 4
1 2
2 3
3 1
3 4

YES

Explanation

The edges $1 \to 2$, $2 \to 3$, and $3 \to 1$ form a directed cycle.