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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Arrays;
import java.util.Set;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    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 void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt();
            Set<Integer> graph[] = new Set[n];
            for (int i = 0; i < n; i++) {
                graph[i] = new HashSet<>();
            }
            for (int i = 0; i < m; i++) {
                graph[in.nextInt() - 1].add(in.nextInt() - 1);
            }
            boolean visited[] = new boolean[n];
            ArrayList<Edge> edges = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (!visited[i]) {
                    if (hasCycle(i, graph, visited, new HashSet<>(), edges)) {
                        break;
                    }
                }
            }
            if (edges.size() == 0) {
                out.println("YES");
                return;
            }
            for (Edge edge : edges) {
                Arrays.fill(visited, false);
                graph[edge.st].remove(edge.end);
                boolean hasCycle = false;
                for (int i = 0; i < n; i++) {
                    if (!visited[i] && hasCycle(i, graph, visited, new HashSet<>())) {
                        hasCycle = true;
                        break;
                    }
                }
                if (!hasCycle) {
                    out.println("YES");
                    return;
                }
                graph[edge.st].add(edge.end);
            }
            out.println("NO");

        }

        private boolean hasCycle(int st, Set<Integer> graph[], boolean visited[], HashSet<Integer> visitedSet, ArrayList<Edge> edges) {
            if (visitedSet.contains(st)) {
                return true;
            }
            if (visited[st]) return false;
            visitedSet.add(st);
            visited[st] = true;
            boolean ans = false;
            for (int child : graph[st]) {
                boolean hasCycle = hasCycle(child, graph, visited, visitedSet, edges);
                if (hasCycle) {
                    edges.add(new Edge(st, child));
                    ans = true;
                    break;
                }
            }
            visitedSet.remove(st);
            return ans;
        }

        private boolean hasCycle(int st, Set<Integer> graph[], boolean visited[], HashSet<Integer> visistedSet) {
            if (visistedSet.contains(st)) {
                return true;
            }
            if (visited[st]) return false;
            visistedSet.add(st);
            visited[st] = true;
            boolean ans = false;
            for (int child : graph[st]) {
                boolean hasCycle = hasCycle(child, graph, visited, visistedSet);
                if (hasCycle) {
                    ans = true;
                    break;
                }
            }
            visistedSet.remove(st);
            return ans;
        }

        private class Edge {
            int st;
            int end;

            public Edge(int st, int child) {
                this.st = st;
                this.end = child;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int nextInt() {
            return readInt();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

