Description

In graph theory, a directed acyclic graph (DAG) is a directed graph with no directed cycles.

Given a directed graph G = (V, E), note that:
- For any two vertices u, v in V, there may not exists path from u to v.
- G doesn't have multiple edges and self-loops.

V is a set of n vertices, denoted by 1, 2, ..., n.

E is a set of m edges, and each edge is represented by two ordered vertices u, v, which denotes an edge from vertex u to vertex v.

Please answer if graph G is a directed acyclic graph (DAG) or not.

Input

The first line contains two integers n and m — the size of V and the size of E.

Each of the following m lines contains two integers u_i and v_i, being an edge in E.

Restrictions

- 2 ≤ n ≤ 10⁵
- 1 ≤ m ≤ min(n * (n - 1) / 2, 2 * 10⁵)
- 1 ≤ u_i, v_i ≤ n, u_i ≠ v_i for 1 ≤ i ≤ m

Output

Output one line.

If graph G is DAG, output "YES". Otherwise, output "NO".

Sample Input  Download

Sample Output  Download

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