You are given a [directed graph](https://en.wikipedia.org/wiki/Directed_graph) consisting of n vertices and m edges (each edge is directed, so it can be traversed in only one direction). You are allowed to remove at most one edge from it.

Can you make this graph [acyclic](https://en.wikipedia.org/wiki/Directed_acyclic_graph) by removing at most one edge from it? A directed graph is called acyclic iff it doesn't contain any cycle (a non-empty path that starts and ends in the same vertex).

Input

The first line contains two integers n and m (2 ≤ n ≤ 500, 1 ≤ m ≤ min(n(n - 1), 100000)) — the number of vertices and the number of edges, respectively.

Then m lines follow. Each line contains two integers u and v denoting a directed edge going from vertex u to vertex v (1 ≤ u, v ≤ n, u ≠ v). Each ordered pair (u, v) is listed at most once (there is at most one directed edge from u to v).

Output

If it is possible to make this graph acyclic by removing at most one edge, print YES. Otherwise, print NO.

Examples

Input

3 4
1 2
2 3
3 2
3 1


Output

YES


Input

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


Output

NO

Note

In the first example you can remove edge <image>, and the graph becomes acyclic.

In the second example you have to remove at least two edges (for example, <image> and <image>) in order to make the graph acyclic.
#include <bits/stdc++.h>
using namespace std;
int to[100005], ne[100005];
int hd[505], n, m, tot;
int id[505], a[505];
inline bool solve(int x) {
  memcpy(a, id, sizeof(id));
  a[x]--, tot = 0;
  queue<int> q;
  for (int i = 1; i <= n; i++)
    if (!a[i]) q.push(i), tot++;
  while (!q.empty()) {
    x = q.front(), q.pop();
    for (int i = hd[x]; i; i = ne[i])
      if (!(--a[to[i]])) {
        q.push(to[i]);
        tot++;
      }
  }
  return (tot == n);
}
int main() {
  int uu, vv;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    scanf("%d%d", &uu, &vv);
    id[vv]++, to[i] = vv, ne[i] = hd[uu], hd[uu] = i;
  }
  for (int i = 1; i <= n; i++)
    if (solve(i)) {
      puts("YES");
      return 0;
    }
  puts("NO");
  return 0;
}
