Hexadecimal likes drawing. She has drawn many graphs already, both directed and not. Recently she has started to work on a still-life «interesting graph and apples». An undirected graph is called interesting, if each of its vertices belongs to one cycle only — a funny ring — and does not belong to any other cycles. A funny ring is a cycle that goes through all the vertices just once. Moreover, loops are funny rings too.

She has already drawn the apples and some of the graph edges. But now it is not clear, how to connect the rest of the vertices to get an interesting graph as a result. The answer should contain the minimal amount of added edges. And furthermore, the answer should be the lexicographically smallest one. The set of edges (x1, y1), (x2, y2), ..., (xn, yn), where xi ≤ yi, is lexicographically smaller than the set (u1, v1), (u2, v2), ..., (un, vn), where ui ≤ vi, provided that the sequence of integers x1, y1, x2, y2, ..., xn, yn is lexicographically smaller than the sequence u1, v1, u2, v2, ..., un, vn. If you do not cope, Hexadecimal will eat you. ...eat you alive.

Input

The first line of the input data contains a pair of integers n and m (1 ≤ n ≤ 50, 0 ≤ m ≤ 2500) — the amount of vertices and edges respectively. The following lines contain pairs of numbers xi and yi (1 ≤ xi, yi ≤ n) — the vertices that are already connected by edges. The initial graph may contain multiple edges and loops.

Output

In the first line output «YES» or «NO»: if it is possible or not to construct an interesting graph. If the answer is «YES», in the second line output k — the amount of edges that should be added to the initial graph. Finally, output k lines: pairs of vertices xj and yj, between which edges should be drawn. The result may contain multiple edges and loops. k can be equal to zero.

Examples

Input

3 2
1 2
2 3


Output

YES
1
1 3

import java.io.*;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

/**
 * CodeForces 9E - Interesting Graph and Apples
 * Created by Darren on 14-10-6.
 *
 * Tag: Euler circuit, graph, disjoint set
 */
public class Main {
    Reader in = new Reader(System.in);
    PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    int n, m;
    List<List<Integer>> graph;
    DisjointSets ds;

    void run() throws IOException {
        n = in.nextInt();
        m = in.nextInt();
        graph = new ArrayList<List<Integer>>(n+1);
        graph.add(null);
        for (int i = 1; i <= n; i++)
            graph.add(new ArrayList<Integer>());
        ds = new DisjointSets(n+1);
        boolean hasCycle = false;
        for (int i = 0; i < m; i++) {
            int u = in.nextInt(), v = in.nextInt();
            graph.get(u).add(v);
            graph.get(v).add(u);
            hasCycle |= !ds.union(u, v);
        }

        if (checkRing()) {
            out.println("YES");
            out.println(0);
        } else {
            if (!verify() || hasCycle) {
                out.println("NO");
            } else {
                out.println("YES");
                out.println(n-m);
                addEdges();
            }
        }
        out.flush();
    }

    boolean checkRing() {
        if (m != n)
            return false;
        for (int i = 1; i <= n; i++) {
            if (graph.get(i).size() != 2)
                return false;
        }
        int root = ds.find(1);
        for (int i = 2; i <= n; i++) {
            if (ds.find(i) != root)
                return false;
        }
        return true;
    }

    boolean verify() {
        if (m >= n)
            return false;
        for (int i = 1; i <= n; i++) {
            if (graph.get(i).size() > 2)
                return false;
        }
        return true;
    }

    void addEdges() {
        for (int u = 1; u < n; u++) {
            if (graph.get(u).size() == 2)
                continue;
            for (int v = u+1; v <= n; v++) {
                if (graph.get(v).size() == 2)
                    continue;
                if (ds.find(u) != ds.find(v)) {
                    graph.get(u).add(v);
                    graph.get(v).add(u);
                    ds.union(u, v);
                    out.printf("%d %d\n", u, v);
                    if (graph.get(u).size() == 2)
                        break;
                }
            }
        }

        if (n == 1) {
            out.printf("%d %d\n", 1, 1);
        } else {
            for (int u = 1; u < n; u++) {
                if (graph.get(u).size() == 2)
                    continue;
                for (int v = u+1; v <= n; v++) {
                    if (graph.get(v).size() == 2)
                        continue;
                    out.printf("%d %d\n", u, v);
                }
            }
        }
    }

    class DisjointSets {

        private int[] array;

        public DisjointSets(int numElements) {
            array = new int [numElements];
            for (int i = 0; i < array.length; i++) {
                array[i] = -1;
            }
        }

        public boolean union(int x1, int x2) {
            int root1 = find(x1), root2 = find(x2);
            if (root1 == root2)     // They are in the same set
                return false;
            if (array[root2] < array[root1]) {
                array[root1] = root2;       // root2 is taller; make root2 new root
            } else if (array[root1] < array[root2]) {
                array[root2] = root1;       // root1 is taller; make root1 new root
            } else {
                // They are of the same height; make root1 new root and the new tree is taller
                array[root2] = root1;
                array[root1]--;
            }
            return true;
        }

        public int find(int x) {
            if (array[x] < 0) {
                return x;                         // x is the root of the tree; return it
            } else {
                // Find out who the root is; compress path by making the root x's parent.
                array[x] = find(array[x]);
                return array[x];                                       // Return the root
            }
        }
    }

    static class Reader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public Reader(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        /** get next word */
        String nextToken() throws IOException {
            while ( ! tokenizer.hasMoreTokens() ) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer( reader.readLine() );
            }
            return tokenizer.nextToken();
        }

        String readLine() throws IOException {
            return reader.readLine();
        }

        int nextInt() throws IOException {
            return Integer.parseInt( nextToken() );
        }

        long nextLong() throws IOException {
            return Long.parseLong( nextToken() );
        }

        double nextDouble() throws IOException {
            return Double.parseDouble( nextToken() );
        }
    }
}
