Description

You are given a 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 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 \(m\)

\(\left(2?\le?n?\le?500, 1?\le m \le \min\left(n \cdot\left(n?-?1\right),?100000\right)\right)\) — 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

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 \(2 \rightarrow 3\) and the graph becomes acyclic.

In the second example you have to remove at least two edges (for example, \(2 \rightarrow 1\) and \(2 \rightarrow 3\)) in order to make the graph acyclic.

題解

有向圖無環當且僅當存在拓撲序，而刪掉邊\(\left(u, v\right)\)的作用是使點\(v\)的入度減一，盡管邊的數量是\(100000\)，但是對於同一個頂點，刪掉不同入邊的效果是等價的，所以我們只需要枚舉每個頂點，將其入度減一，檢查是否存在拓撲序即可。

#include <bits/stdc++.h>
using namespace std;
const int maxn = 511;
vector<int> w[maxn];
int d1[maxn], d2[maxn];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    w[u].push_back(v);
    ++d1[v];
  }
  bool fg = false;
  for (int i = 1; i <= n; ++i) {
    if (d1[i] == 0) continue;
    for (int j = 1; j <= n; ++j)
      d2[j] = d1[j];
    --d2[i];
    queue<int> que;
    int ct = 0;
    for (int j = 1; j <= n; ++j) {
      if (!d2[j]) {
        que.push(j);
        ++ct;
      }
    }
    while (!que.empty()) {
      int u = que.front();
      que.pop();
      for (int v : w[u]) {
        if (--d2[v] == 0) {
          que.push(v);
          ++ct;
        }
      }
    }
    if (ct == n) {
      fg = true;
      break;
    }
  }
  puts(fg ? "YES" : "NO");
  return 0;
}

CodeForces 915D Almost Acyclic Graph