Codeforces 915D - Almost Acyclic Graph（拓扑排序）

D. Almost Acyclic Graph

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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).

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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 , and the graph becomes acyclic.

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

#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define clr(a) memset(a,0,sizeof(a))

const int MAXN = 1e5+10;
const int INF = 0x3f3f3f3f;
const int N = 101;

int n,m;
int in[MAXN],ins[MAXN];
vector<int>g[MAXN];

bool top_sort(int x){
    for(int i=0;i<=n;i++){
        in[i] = ins[i];
    }
    int num=0;
    in[x] --;
    queue<int>q;
    for(int i=1;i<=n;i++){
        if(in[i] == 0) {
            q.push(i);
            num++;
        }
    }
    while(!q.empty()){
        int top = q.front();
        q.pop();
        for(int j=0;j<g[top].size();j++){
            if(!(--in[g[top][j]])) {
                q.push(g[top][j]);
                num++;
            }
        }
    }
    if(num == n)    return true;
    else return false;
}

int main(){
    clr(in);
    scanf("%d%d",&n,&m);
    int x,y;
    for(int i=0;i<m;i++){
        scanf("%d%d",&x,&y);
        g[x].push_back(y);
        ins[y] ++;
    }
    for(int i=1;i<=n;i++){
        if(top_sort(i)){
            puts("YES");return 0;
        }
    }
    puts("NO");
    return 0;
}