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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class E {
static ArrayList<Integer>[] adj;
static int cycleHead;
static int []visited,p;

static ArrayList<Integer> cycle;

public static boolean dfs(int u,int du,int dv)
{
	
	visited[u]=1;

	boolean ans=false;
	for(int v:adj[u])
	{
		if(u==du && v==dv)
			continue;
		
		if(visited[v]==1)
		{
			ans=true;
			
			return true;
		}
		else if(visited[v]==0)
			ans|=dfs(v,du,dv);
	}
	visited[u]=2;
	
	return ans;
}
public static void helper(int u,int head)
{
		if(u==head)
		{
			cycle.add(u);
			return;
		}
		cycle.add(u);
		helper(p[u],head);
}
public static boolean getCycle(int u)
{
	
	boolean done=false;
	visited[u]=1;
	
	for(int v:adj[u])
	{
		
		if(done)
			return true;
		if(visited[v]==1)
		{
			cycle.add(v);
			helper(u,v);
			done=true;
			return done;
			
		}
		else if(visited[v]==0)
		{	
			p[v]=u;
			done|=getCycle(v);
		}	
	}
	visited[u]=2;
	return done;
	
}

	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),m=sc.nextInt();
		adj=new ArrayList[n];
		
		for(int i=0;i<n;i++)
			adj[i]=new ArrayList();
		p=new int [n];
		while(m-->0)
		{	
			int u=sc.nextInt()-1,v=sc.nextInt()-1;
			adj[u].add(v);
			
		}	
		visited=new int [n];
		cycle=new ArrayList();
		
		
		for(int i=0;i<n;i++)
		{	
			if(visited[i]==0)
			{
				if(getCycle(i))
					break;
				else
					cycle.clear();
			}
		}	
		
		if(cycle.size()==0)
		{
			System.out.println("YES");
			return;
		}
		for(int i=cycle.size()-1;i>0;i--)
		{
			boolean hasCycle=false;
			Arrays.fill(visited, 0);
			int du=cycle.get(i);int dv=cycle.get(i-1);
			for(int j=0;j<n;j++)
				if(visited[j]==0)
					hasCycle|=dfs(j,du,dv);
			if(!hasCycle)
			{
				System.out.println("YES");
				return;
			}
		}
		
		System.out.println("NO");
		
		
	}

	static class edge
	{
		int u;int v; //from u to v
		public edge(int x,int y)
		{
			u=x;v=y;
		}
	}
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}
		
		public long nextLong() throws IOException {return Long.parseLong(next());}

		public String nextLine() throws IOException {return br.readLine();}
		
		public double nextDouble() throws IOException
		{
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if(x.charAt(0) == '-')
			{
				neg = true;
				start++;
			}
			for(int i = start; i < x.length(); i++)
				if(x.charAt(i) == '.')
				{
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				}
				else
				{
					sb.append(x.charAt(i));
					if(dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg?-1:1);
		}
		
		public boolean ready() throws IOException {return br.ready();}


	}

}
