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;
using cd = complex<double>;
const long long INF = 1e18;
const long long mod = 998244353;
const double Pi = acos(-1);
void Fastio() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
}
int n, m;
int Vis[505], par[505];
vector<int> Adj[505];
vector<int> Cyc;
bool ok;
void DFS(int node) {
  Vis[node] = 1;
  for (auto x : Adj[node]) {
    if (Vis[x] == 0) {
      par[x] = node;
      DFS(x);
    } else if (Vis[x] == 1 && Cyc.size() == 0) {
      int temp = node;
      while (true) {
        Cyc.emplace_back(temp);
        if (temp == x) {
          break;
        }
        temp = par[temp];
      }
    }
  }
  Vis[node] = 2;
}
void DFS2(int node, int u, int v) {
  Vis[node] = 1;
  for (auto x : Adj[node]) {
    if (u == node && v == x) {
      continue;
    }
    if (Vis[x] == 0) {
      DFS2(x, u, v);
    }
    if (Vis[x] == 1) {
      ok = false;
    }
  }
  Vis[node] = 2;
}
signed main() {
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    Adj[u].emplace_back(v);
  }
  for (int i = 1; i <= n; i++) {
    if (!Vis[i]) {
      DFS(i);
    }
  }
  if (Cyc.size() == 0) {
    cout << "YES";
    return 0;
  }
  for (int i = 0; i < Cyc.size(); i++) {
    int x = Cyc[i], y = Cyc[(i + 1) % Cyc.size()];
    for (int i = 1; i <= n; i++) {
      Vis[i] = 0;
    }
    ok = true;
    for (int i = 1; i <= n; i++) {
      if (!Vis[i]) DFS2(i, y, x);
    }
    if (ok) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
}
