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

Input

4 3
1 2
2 3
3 4

Output

NO

Explanation

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

Example 2

Input

4 4
1 2
2 3
3 1
3 4

Output

YES

Explanation

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