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;
void fast() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
vector<vector<int> > adj(1e4);
vector<int> vis(1e4, 0);
vector<pair<int, int> > s;
int POP = 0, y = -1, Done = 0;
int Mark = 1;
int n, m;
void initialize() {
  fill(vis.begin(), vis.end(), 0);
  Mark = 1;
}
void check(int u) {
  vis[u] = 1;
  for (auto x : adj[u]) {
    if (x == -1) continue;
    if (vis[x] == 1) Mark = 0;
    if (!vis[x]) {
      check(x);
    }
  }
  vis[u] = 2;
}
void dfs(int u) {
  vis[u] = 1;
  if (Done) return;
  for (auto x : adj[u]) {
    if (!vis[x]) dfs(x);
    if (vis[x] == 1) {
      POP = 1;
      y = x;
    }
    if (POP && (!Done)) {
      s.push_back(make_pair(u, x));
      if (u == y) {
        Done = 1;
        break;
      }
      break;
    }
  }
  vis[u] = 2;
}
int main() {
  cin >> n >> m;
  for (long long i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    adj[x].push_back(y);
  }
  for (long long i = 1; i < n + 1; i++) {
    if (Done) break;
    if (!vis[i]) dfs(i);
  }
  if (s.empty()) {
    cout << "YES";
    return 0;
  }
  for (auto k : s) {
    int x = k.first, y = k.second;
    auto p = adj[x].begin();
    while (p != adj[x].end()) {
      if ((*p) == y) {
        (*p) = -1;
      }
      p++;
    }
    initialize();
    for (long long i = 1; i < n + 1; i++) {
      if (!vis[i]) check(i);
    }
    if (Mark) {
      cout << "YES";
      return 0;
    }
    p = adj[x].begin();
    while (p != adj[x].end()) {
      if ((*p) == -1) {
        (*p) = y;
      }
      p++;
    }
  }
  cout << "NO";
}
