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.
//package info.stochastic;

import java.io.*;
import java.util.*;

public class D {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {

        public static List<Integer> cycleDfs(Map<Integer, List<Integer>> g, Map<Integer, Integer> visited, int start) {

            if (visited.containsKey(start) && visited.get(start) == 1) {
                List<Integer> cycle = new ArrayList<>();
                cycle.add(start);
                return cycle;
            }

            visited.put(start, 1);

            if (g.containsKey(start)) {
                for (Integer nextEdge: g.get(start)) {
                    if (!visited.containsKey(nextEdge) || visited.get(nextEdge) == 1) {
                        List<Integer> cycle = cycleDfs(g, visited, nextEdge);
                        if (cycle != null) {
                            cycle.add(start);
                            return cycle;
                        }
                    }
                }
            }
            visited.put(start, 2);
            return null;
        }

        public static List<Integer> findCycle(Map<Integer, List<Integer>> g, Set<Integer> nodes) {
            //System.out.println(g.keySet().size());
            Map<Integer, Integer> visited = new HashMap<>();
            for (Integer vertex: nodes) {
                if (!visited.containsKey(vertex)) {
                    List<Integer> cycle  = cycleDfs(g, visited, vertex);
                    if (cycle != null) {
                        return cycle;
                    }
                }
            }
            return null;
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();

            Map<Integer, List<Integer>> g = new HashMap<>();
            Set<Integer> nodes = new HashSet<>();
            for (int i = 0; i < m; i++) {
                int from = in.nextInt();
                int to = in.nextInt();
                nodes.add(from);
                nodes.add(to);

                List<Integer> edges = new ArrayList<>();
                if (g.containsKey(from)) {
                    edges = g.get(from);
                }
                edges.add(to);
                g.put(from, edges);
            }

            List<Integer> cycle = findCycle(g, nodes);

            if (cycle == null) {
                out.print("YES");
                return;
            }

            Collections.reverse(cycle);
            for (int i = 0; i < cycle.size() - 1; i++) {
                int from = cycle.get(i);
                int to = cycle.get(i + 1);

                List<Integer> edges = g.get(from);
                edges.remove(new Integer(to));
                if (findCycle(g, nodes) == null) {
                    out.print("YES");
                    return;
                }
                edges.add(to);
            }

            out.print("NO");
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}
