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 n, m, G[517][517], deg[517], x, y, die[517], aim;
queue<int> q;
namespace ck {
int die[517], deg[517];
queue<int> q;
int realmain(int x, int y, int aim) {
  --deg[y];
  for (; !q.empty(); q.pop())
    ;
  q.push(y);
  for (; !q.empty();) {
    x = q.front();
    q.pop();
    die[x] = 1;
    --aim;
    for (int i = 1; i <= n; ++i)
      if (G[x][i] && !die[i])
        if (!--deg[i]) q.push(i);
  }
  return !aim;
}
}  // namespace ck
int main() {
  scanf("%d%d", &n, &m);
  aim = n;
  for (int i = m; i--;) scanf("%d%d", &x, &y), G[x][y] = 1, ++deg[y];
  for (int i = 1; i <= n; ++i)
    if (!deg[i]) q.push(i);
  for (; !q.empty();) {
    x = q.front();
    q.pop();
    die[x] = 1;
    --aim;
    for (int i = 1; i <= n; ++i)
      if (G[x][i])
        if (!--deg[i]) q.push(i);
  }
  if (!aim) return 0 * puts("YES");
  for (int i = 1; i <= n; ++i)
    if (!die[i] && deg[i] == 1) {
      for (x = 1; !(!die[x] && G[x][i]); ++x)
        ;
      memcpy(ck::die, die, sizeof die);
      memcpy(ck::deg, deg, sizeof deg);
      if (ck::realmain(x, i, aim)) return 0 * puts("YES");
    }
  puts("NO");
}
