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;
long long n, m, u, v, vis[502], tim[100005], ttm, root;
vector<long long> adj[502];
vector<pair<long long, long long> > cycle;
pair<long long, long long> p;
bool cy = false, fn = false;
void dfs(long long node) {
  if (vis[node] == 2 || cy) return;
  if (vis[node] == 1) {
    cy = true;
    root = node;
    return;
  }
  vis[node] = 1;
  for (auto x : adj[node]) dfs(x);
  if (!cy) vis[node] = 2;
}
void dfs2(long long node) {
  if (vis[node] == 2 || cy) return;
  if (vis[node] == 1) {
    cy = true;
    root = node;
    return;
  }
  vis[node] = 1;
  for (auto x : adj[node]) {
    pair<long long, long long> tmp = {node, x};
    if (p == tmp) continue;
    dfs2(x);
  }
  if (!cy) vis[node] = 2;
}
void print(long long node) {
  if (node == root && cycle.size()) {
    fn = true;
    return;
  }
  for (auto x : adj[node]) {
    if (fn) return;
    if (vis[x] != 1) continue;
    cycle.push_back({node, x});
    if (fn) return;
    print(x);
  }
}
bool check() {
  memset(vis, 0, sizeof(vis));
  cy = false;
  for (int i = 1; i <= n; i++)
    if (!vis[i]) dfs2(i);
  if (cy == false)
    return true;
  else
    return false;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    cin >> u >> v;
    adj[u].push_back(v);
  }
  for (long long i = 1; i <= n; i++) {
    if (vis[i]) continue;
    dfs(i);
    if (root != 0) break;
  }
  print(root);
  if (!cycle.size()) {
    cout << "YES" << endl;
    return 0;
  }
  for (auto x : cycle) {
    p = x;
    if (check()) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}
