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;
using i64 = long long int;
using ii = pair<int, int>;
using ii64 = pair<i64, i64>;
vector<ii> edges[501];
vector<int> cycles;
int n, m;
bool visited[501];
bool finded[501];
bool dfs(int now, int removed) {
  if (finded[now]) return true;
  finded[now] = true;
  visited[now] = true;
  for (auto& e : edges[now]) {
    if (e.second == removed) continue;
    if (visited[e.first]) return false;
    if (!finded[e.first] && !dfs(e.first, removed)) return false;
  }
  visited[now] = false;
  return true;
}
bool getCycle(int now) {
  if (finded[now]) return false;
  finded[now] = true;
  visited[now] = true;
  for (auto& e : edges[now]) {
    cycles.push_back(e.second);
    if (visited[e.first]) return true;
    if (!finded[e.first] && getCycle(e.first)) return true;
    cycles.pop_back();
  }
  visited[now] = false;
  return false;
}
bool check(int removed) {
  memset(visited, false, sizeof(visited));
  memset(finded, false, sizeof(finded));
  for (int i = 1; i <= n; i++) {
    if (!dfs(i, removed)) return false;
  }
  return true;
}
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 0; i < m; i++) {
    int u, v;
    scanf("%d %d", &u, &v);
    edges[u].emplace_back(v, i);
  }
  for (int i = 1; i <= n; i++) {
    if (getCycle(i)) break;
  }
  if (cycles.empty()) {
    printf("YES\n");
    return 0;
  }
  for (auto& c : cycles) {
    if (check(c)) {
      printf("YES\n");
      return 0;
    }
  }
  printf("NO\n");
  return 0;
}
