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.*;

public class CF {

	boolean[] was;

	ArrayList<Integer>[] g;

	boolean go(int v, int p) {
		was[v] = true;
		for (int x : g[v])
			if (x != p)
				if (was[x])
					return true;
				else
					go(x, v);
		return false;
	}

	boolean isCycle(ArrayList<Integer>[] g) {
		int n = g.length;
		was = new boolean[n];
		boolean res = false;
		this.g = g;
		for (int i = 0; i < n; i++)
			if (!was[i])
				res |= go(i, -1);
		return res;
	}

	ArrayList<Integer> ans1 = new ArrayList<>();
	ArrayList<Integer> ans2 = new ArrayList<>();

	boolean find(ArrayList<Integer>[] g) {
		int m = 0;
		int n = g.length;
		for (int i = 0; i < n; i++)
			m += g[i].size();
		m /= 2;
		if (m > n)
			return false;
		boolean cycle = isCycle(g);
		if (m == n) {
			if (!cycle)
				return false;
			for (int i = 0; i < n; i++)
				if (g[i].size() != 2)
					return false;
			was = new boolean[n];
			go(0, -1);
			for (int i = 0; i < n; i++)
				if (!was[i])
					return false;
			return true;
		}
		for (int fr = 0; fr < n; fr++)
			for (int to = fr; to < n; to++) {
				g[fr].add(to);
				g[to].add(fr);
				ans1.add(fr);
				ans2.add(to);
				if (find(g)) {
					return true;
				} else {
					g[fr].remove(g[fr].size() - 1);
					g[to].remove(g[to].size() - 1);
					ans1.remove(ans1.size() - 1);
					ans2.remove(ans2.size() - 1);
				}
			}
		return false;
	}

	class Dsu {
		int[] p;

		Dsu(int n) {
			p = new int[n];
			for (int i = 0; i < n; i++)
				p[i] = i;
		}

		int get(int v) {
			return v == p[v] ? v : (p[v] = get(p[v]));
		}

		void union(int v, int u) {
			v = get(v);
			u = get(u);
			if (u == v)
				return;
			p[v] = u;
		}
	}

	void realSolve() {
		int n = in.nextInt();
		int m = in.nextInt();
		ArrayList<Integer>[] g = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			g[i] = new ArrayList<>();
		}
		for (int i = 0; i < m; i++) {
			int fr = in.nextInt() - 1;
			int to = in.nextInt() - 1;
			g[fr].add(to);
			g[to].add(fr);
		}
		if (n <= 5 || m >= n) {
			if (!find(g)) {
				out.println("NO");
			} else {
				out.println("YES");
				out.println(ans1.size());
				for (int i = 0; i < ans1.size(); i++)
					out.println((ans1.get(i) + 1) + " " + (ans2.get(i) + 1));
			}
		} else {
			Dsu dsu = new Dsu(n);
			for (int i = 0; i < n; i++)
				for (int x : g[i])
					dsu.union(i, x);
			for (int fr = 0; fr < n; fr++)
				for (int to = fr; to < n; to++)
					if (m < n && dsu.get(fr) != dsu.get(to) && g[fr].size() < 2
							&& g[to].size() < 2) {
						g[fr].add(to);
						g[to].add(fr);
						ans1.add(fr);
						ans2.add(to);
						dsu.union(fr, to);
						m++;
					}
			for (int fr = 0; fr < n; fr++)
				for (int to = fr + 1; to < n; to++)
					if (m == n - 1 && g[fr].size() == 1 && g[to].size() == 1) {
						g[fr].add(to);
						g[to].add(fr);
						ans1.add(fr);
						ans2.add(to);
						dsu.union(fr, to);
						m++;
					}
			//for (int i = 0; i < ans1.size(); i++) {
			//	System.err.println(ans1.get(i) + " " + ans2.get(i));
			//}
			was = new boolean[n];
			this.g = g;
			go(0, -1);
			boolean ok = true;
			for (int i = 0; i < n; i++)
				if (g[i].size() != 2)
					ok = false;
			for (int i = 0; i < n; i++)
				if (!was[i])
					ok = false;
			if (!ok) {
				out.println("NO");
			} else {
				out.println("YES");
				out.println(ans1.size());
				for (int i = 0; i < ans1.size(); i++)
					out.println((ans1.get(i) + 1) + " " + (ans2.get(i) + 1));
			}
		}
	}

	private class InputReader {
		StringTokenizer st;
		BufferedReader br;

		public InputReader(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public InputReader(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				String s;
				try {
					s = br.readLine();
				} catch (IOException e) {
					return null;
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

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

		double nextDouble() {
			return Double.parseDouble(next());
		}

		boolean hasMoreElements() {
			while (st == null || !st.hasMoreElements()) {
				String s;
				try {
					s = br.readLine();
				} catch (IOException e) {
					return false;
				}
				st = new StringTokenizer(s);
			}
			return st.hasMoreElements();
		}

		long nextLong() {
			return Long.parseLong(next());
		}
	}

	InputReader in;
	PrintWriter out;

	void solve() {
		in = new InputReader(new File("object.in"));
		try {
			out = new PrintWriter(new File("object.out"));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}

		realSolve();

		out.close();
	}

	void solveIO() {
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);

		realSolve();

		out.close();

	}

	public static void main(String[] args) {
		new CF().solveIO();
	}
}