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;
vector<int> path;
int N, M;
vector<int> adj[501];
bool foundCycle = false;
int inCycle;
bool visited[501];
bool done = false;
int state[501];
void check(int node, int x, int y) {
  if (state[node] == 2) return;
  state[node] = 1;
  for (int i = 0; i < adj[node].size(); i++) {
    if (foundCycle) {
      state[node] = 2;
      return;
    }
    if (x == node && y == adj[node][i]) continue;
    if (state[adj[node][i]] == 1) {
      inCycle = node;
      foundCycle = true;
      state[node] = 2;
      return;
    } else if (state[adj[node][i]] == 0)
      check(adj[node][i], x, y);
  }
  state[node] = 2;
}
void dfs(int node) {
  state[node] = 1;
  for (int i = 0; i < adj[node].size(); i++) {
    if (done) return;
    if (state[adj[node][i]] == 0) {
      path.push_back(adj[node][i]);
      dfs(adj[node][i]);
    } else if (state[adj[node][i]] == 1) {
      path.push_back(adj[node][i]);
      done = true;
      return;
    }
    if (done) return;
  }
  if (done) return;
  state[node] = 2;
  path.pop_back();
}
int main() {
  cin >> N >> M;
  for (int i = 0; i < M; i++) {
    int x, y;
    cin >> x >> y;
    adj[x].push_back(y);
  }
  for (int i = 1; i <= N; i++) {
    check(i, -1, -1);
    if (foundCycle) break;
  }
  if (!foundCycle) {
    cout << "YES" << endl;
    return 0;
  }
  for (int j = 1; j <= N; j++) state[j] = 0;
  path.push_back(inCycle);
  dfs(inCycle);
  for (int i = (int)path.size() - 1; i > 0; i--) {
    if (path[i] == path[path.size() - 1] && i != path.size() - 1) break;
    foundCycle = false;
    for (int j = 1; j <= N; j++) state[j] = 0;
    for (int j = 1; j <= N; j++) check(j, path[i - 1], path[i]);
    if (!foundCycle) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}
