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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Stack;
import java.util.ArrayList;
import java.util.List;
import java.util.Vector;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author qianyin
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            final int n = in.nextInt();
            final int m = in.nextInt();
            final V[] vs = init(n + 1);
            final List<E> es = new ArrayList<>();
            for (int i = 0; i < m; i++) {
                V u = vs[in.nextInt()];
                V v = vs[in.nextInt()];
                u.add(v);
                es.add(new E(u, v));
            }

            Stack<V> trail = new Stack<>();
            for (V v : vs) v.state = 0;
            for (V v : vs) {
                if (v.state == 0 && !dfs(v, trail)) {
                    break;
                }
            }

            if (trail.isEmpty()) {
                out.println("YES");
                return;
            }

            V y = trail.pop();
            while (!trail.isEmpty()) {
                V x = trail.pop();
                E e = new E(x, y);

                boolean hasLoop = false;
                for (V v : vs) v.state = 0;
                for (V v : vs) {
                    if (v.state == 0 && !dfs(v, e)) {
                        hasLoop = true;
                        break;
                    }
                }

                if (!hasLoop) {
                    out.println("YES");
                    return;
                } else {
                    y = x;
                }
            }

            out.println("NO");
        }

        private V[] init(int size) {
            V[] vs = new V[size];
            for (int i = 0; i < size; i++) {
                vs[i] = new V();
            }
            return vs;
        }

        private boolean dfs(V u, Stack<V> stack) {
            u.state = 1;
            stack.push(u);
            for (V v : u) {
                if (v.state == 1) {
                    stack.push(v);
                    return false;
                } else if (v.state == 0 && !dfs(v, stack)) {
                    return false;
                }
            }
            u.state = 2;
            stack.pop();
            return true;
        }

        private boolean dfs(V u, E hide) {
            u.state = 1;
            for (V v : u) {
                if (hide == null || hide.from != u || hide.to != v) {
                    if (v.state == 1 || v.state == 0 && !dfs(v, hide)) {
                        return false;
                    }
                }
            }
            u.state = 2;
            return true;
        }

        class V extends ArrayList<V> implements List<V> {
            int state;

        }

        class E {
            V from;
            V to;

            E(V from, V to) {
                this.from = from;
                this.to = to;
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

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

        }

    }
}

