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, pi;
vector<int> adj[550];
vector<int> cycle;
bool done;
bool visited[550], inStack[550];
bool dfs(int u) {
  inStack[u] = true;
  visited[u] = true;
  for (int i = 0; i < ((int)(adj[u]).size()); ++i) {
    if (inStack[adj[u][i]]) {
      pi = adj[u][i];
      cycle.push_back(pi);
      return true;
    }
    if (!visited[adj[u][i]]) {
      if (dfs(adj[u][i])) {
        if (!done && adj[u][i] != pi) {
          cycle.push_back(adj[u][i]);
        } else if (adj[u][i] == pi) {
          done = true;
        }
        return true;
      }
    }
  }
  inStack[u] = false;
  return false;
}
bool detectCycle(int v, int a, int b) {
  visited[v] = true;
  inStack[v] = true;
  for (int i = 0; i < ((int)(adj[v]).size()); ++i) {
    if (v == a && adj[v][i] == b) continue;
    if (inStack[adj[v][i]]) {
      return true;
    }
    if (!visited[adj[v][i]]) {
      if (detectCycle(adj[v][i], a, b)) return true;
    }
  }
  inStack[v] = false;
  return false;
}
int main(int argc, char const* argv[]) {
  cin >> n >> m;
  int u, v;
  for (int i = 0; i < (m); ++i) {
    cin >> u >> v;
    adj[u].push_back(v);
  }
  bool fnd = false;
  for (int i = 1; i <= (n); ++i) {
    if (!visited[i]) {
      if (dfs(i)) {
        fnd = true;
        break;
      }
    }
  }
  if (!fnd) {
    cout << "YES" << endl;
    return 0;
  }
  cycle.push_back(cycle[0]);
  for (int i = 0; i < ((int)(cycle).size() - 1); ++i) {
    fnd = false;
    memset(visited, 0, sizeof(visited));
    memset(inStack, 0, sizeof(inStack));
    for (int j = 1; j <= (n); ++j) {
      if (!visited[j]) {
        if (detectCycle(j, cycle[i + 1], cycle[i])) {
          fnd = true;
          break;
        }
      }
    }
    if (!fnd) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}
