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;
bool dfs(int index, const vector<vector<int>>& e, const pair<int, int>& no_edge,
         int color[], stack<int>& p) {
  color[index] = 1;
  p.push(index);
  for (int next : e[index]) {
    if (index == no_edge.first && next == no_edge.second) {
      continue;
    }
    if (color[next] == 1) {
      p.push(next);
      return true;
    } else if (color[next] == 0) {
      if (dfs(next, e, no_edge, color, p)) {
        return true;
      }
    }
  }
  p.pop();
  color[index] = 2;
  return false;
}
bool has_cycle(int n, const vector<vector<int>>& e,
               const pair<int, int>& no_edge) {
  int color[n + 1];
  for (int i = 0; i < n + 1; ++i) {
    color[i] = 0;
  }
  stack<int> p;
  for (int i = 1; i <= n; ++i) {
    if (color[i] == 0) {
      if (dfs(i, e, no_edge, color, p)) {
        return true;
      }
    }
  }
  return false;
}
vector<pair<int, int>> get_cycle(int n, const vector<vector<int>>& e,
                                 const pair<int, int>& no_edge) {
  int color[n + 1];
  for (int i = 0; i < n + 1; ++i) {
    color[i] = 0;
  }
  stack<int> p;
  for (int i = 1; i <= n; ++i) {
    if (color[i] == 0) {
      if (dfs(i, e, no_edge, color, p)) {
        break;
      }
    }
  }
  vector<pair<int, int>> cycle;
  if (!p.empty()) {
    int parent = p.top();
    p.pop();
    int next = parent;
    while (1) {
      cycle.push_back(make_pair(p.top(), next));
      next = p.top();
      p.pop();
      if (next == parent) {
        break;
      }
    }
  }
  return cycle;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  vector<vector<int>> e(n + 1);
  int u, v;
  for (int i = 0; i < m; ++i) {
    cin >> u >> v;
    e[u].push_back(v);
  }
  if (!has_cycle(n, e, make_pair(-1, -1))) {
    cout << "YES";
  } else {
    auto cycle = get_cycle(n, e, make_pair(-1, -1));
    bool has_another_cycle = true;
    for (auto edge : cycle) {
      if (!has_cycle(n, e, edge)) {
        has_another_cycle = false;
        break;
      }
    }
    if (has_another_cycle) {
      cout << "NO";
    } else {
      cout << "YES";
    }
  }
  return 0;
}
