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 const N = 1e5 + 1;
int n, m, color[N], depth[N], deleted;
vector<pair<int, int> > g[N], cycle;
vector<int> simpleCycle;
int go(int u, int D) {
  color[u] = 1;
  depth[u] = D;
  for (auto i : g[u]) {
    if (color[i.first] == 1) {
      simpleCycle.push_back(i.second);
      return depth[i.first];
    }
    if (!color[i.first]) {
      int f = go(i.first, D + 1);
      if (f == -1) return f;
      if (f <= D) {
        simpleCycle.push_back(i.second);
        return f != D ? f : -1;
      }
    }
  }
  color[u] = 2;
}
bool detectCycle(int u) {
  color[u] = 1;
  for (auto i : g[u]) {
    if (i.second == deleted) continue;
    if (color[i.first] == 1 && i.second != deleted) return true;
    if (!color[i.first] && detectCycle(i.first)) return true;
  }
  color[u] = 2;
  return false;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    g[a].push_back(make_pair(b, i));
  }
  bool have = false;
  for (int i = 1; i <= n; ++i) {
    if (!color[i] && go(i, 0) == -1) {
      have = 1;
      break;
    }
  }
  if (!simpleCycle.size()) return puts("YES"), 0;
  for (auto i : simpleCycle) {
    memset(color, 0, sizeof color);
    deleted = i;
    bool yes = true;
    for (int i = 1; i <= n; ++i)
      if (!color[i] && detectCycle(i)) {
        yes = false;
        break;
      }
    if (yes) return puts("YES"), 0;
  }
  puts("NO");
}
