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>
#pragma GCC target("sse,sse2,sse3,sse3,sse4,popcnt,abm,mmx")
using namespace std;
const int mod = 1e9 + 7;
const int N = 5e2 + 5;
vector<int> g[N];
int cl[N];
int b1 = -1, b2 = -1;
int p[N];
int st = -1, en = -1;
int a[N][N];
bool dfs(int v, int pr) {
  cl[v] = 1;
  for (int i = 0; i < g[v].size(); ++i) {
    int to = g[v][i];
    if (v == b1 && to == b2) continue;
    if (cl[to] == 0) {
      p[to] = v;
      if (dfs(to, v)) return true;
    } else if (cl[to] == 1) {
      st = to;
      en = v;
      return true;
    }
  }
  cl[v] = 2;
  return false;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  srand(time(0));
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    g[x].push_back(y);
    a[x][y]++;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
    }
  }
  for (int i = 0; i < n; i++) p[i] = -1;
  st = -1, en = -1;
  for (int i = 0; i < n; i++) {
    if (cl[i]) continue;
    dfs(i, -1);
    if (st != -1) break;
  }
  if (st == -1) {
    cout << "YES";
    return 0;
  }
  set<int> on;
  int it = 0;
  while (st != en && it < n) {
    on.insert(en);
    en = p[en];
    it++;
  }
  on.insert(st);
  vector<pair<int, int> > e;
  for (auto v : on) {
    for (auto x : g[v]) {
      if (on.count(x)) {
        e.push_back({v, x});
      }
    }
  }
  for (auto x : e) {
    b1 = x.first, b2 = x.second;
    for (int i = 0; i < n; i++) cl[i] = 0;
    st = -1;
    en = -1;
    for (int i = 0; i < n; i++) {
      if (cl[i]) continue;
      dfs(i, -1);
      if (st != -1) break;
    }
    if (st == -1) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
  return 0;
}
