Problem: You are given a forest — an undirected graph with n vertices such that each its connected component is a tree.

The diameter (aka "longest shortest path") of a connected undirected graph is the maximum number of edges in the shortest path between any pair of its vertices.

You task is to add some edges (possibly zero) to the graph so that it becomes a tree and the diameter of the tree is minimal possible.

If there are multiple correct answers, print any of them.

Input

The first line contains two integers n and m (1 ≤ n ≤ 1000, 0 ≤ m ≤ n - 1) — the number of vertices of the graph and the number of edges, respectively.

Each of the next m lines contains two integers v and u (1 ≤ v, u ≤ n, v ≠ u) — the descriptions of the edges.

It is guaranteed that the given graph is a forest.

Output

In the first line print the diameter of the resulting tree.

Each of the next (n - 1) - m lines should contain two integers v and u (1 ≤ v, u ≤ n, v ≠ u) — the descriptions of the added edges.

The resulting graph should be a tree and its diameter should be minimal possible.

For m = n - 1 no edges are added, thus the output consists of a single integer — diameter of the given tree.

If there are multiple correct answers, print any of them.

Examples

Input


4 2
1 2
2 3


Output


2
4 2


Input


2 0


Output


1
1 2


Input


3 2
1 3
2 3


Output


2

Note

In the first example adding edges (1, 4) or (3, 4) will lead to a total diameter of 3. Adding edge (2, 4), however, will make it 2.

Edge (1, 2) is the only option you have for the second example. The diameter is 1.

You can't add any edges in the third example. The diameter is already 2.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;

import java.util.*;

public class A_GENERAL {
   
	// for fast output printing  : use printwriter or stringbuilder
	// remember to close pw using pw.close()
	static StringBuilder sb = new StringBuilder();
	static long seive_size = (long) 1e6;
	static String alpha = "abcdefghijklmnopqrstuvwxyz";
    static ArrayList<Integer> primes = new ArrayList<>();
    static boolean[] set = new boolean[(int) seive_size+1];
    static int n, m;
    static ArrayList<Integer>[] adj;
    static boolean[] visited;
    static ArrayDeque<Integer> q = new ArrayDeque<>();
    static final long MOD = 998244353;
    static long[][] arr;
    static int[] dist;
    
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		MyScanner sc = new MyScanner();
		n = sc.nextInt();
		m = sc.nextInt();
		init(n);
		for(int i = 0; i < m; i++) {
			int u = sc.nextInt();
			int v = sc.nextInt();
			adj[u].add(v);
			adj[v].add(u);
		}
		ArrayList<Integer> mids = new ArrayList<>();
		dist = new int[n+1];
		int cen = 1;
		int maxDia = 0;
		for(int i = 1; i <= n; i++) {
			if(!visited[i]) {
				int curr = findMid(i);
				if(maxDia < dist[curr]) {
					maxDia = dist[curr];
					cen = curr;
				}
				mids.add(curr);
			}
		}
		int ans = maxDia;
		ArrayList<Integer> diaList = new ArrayList<>();
		for(int x : mids) {
			if(x != cen) {
				int xDia = (dist[x]+1)/2 + 1 + (maxDia+1)/2;
				diaList.add((dist[x]+1)/2 + 1);
				ans = Math.max(ans, xDia);
			}
		}
		if(diaList.size() > 1) {
			Collections.sort(diaList, Collections.reverseOrder());
			ans = Math.max(ans, diaList.get(0)+diaList.get(1));
		}
		out.println(ans);
		for(int x : mids) {
			if(x != cen) {
				out.println(cen + " " + x);
			}
		}
		out.close();
	}
	public static int findMid(int i) {
		visited[i] = true;
		q.add(i);
		int last = i;
		while(!q.isEmpty()) {
			int u = q.poll();
			for(int v : adj[u]) {
				if(!visited[v]) {
					q.add(v);
					visited[v] = true;
				}
			}
			last = u;
		}
		dist[last] = 0;
		q = new ArrayDeque<>();
		visited = new boolean[n+1];
		int[] parent = new int[n+1];
		q.add(last);
		visited[last] = true;
		while(!q.isEmpty()) {
			int u = q.poll();
			for(int v : adj[u]) {
				if(!visited[v]) {
					visited[v] = true;
					q.add(v);
					dist[v] = dist[u]+1;
					parent[v] = u;
				}
			}
			last = u;
		}
		int dia = dist[last];
		while(dist[last] != (dia+1)/2) {
			last = parent[last];
		}
		dist[last] = dia;
		return last;
	}
	
	public static void dfs(int u) {
		visited[u] = true;
		for(int v : adj[u]) {
			if(!visited[v]) {
				dfs(v);
			}
		}
	}

	public static class Pair {
		long f;
		long s;
		Pair(long f, long s) {
			this.f = f;
			this.s = s;
		}
	}
	public static void init(int n) {
    	adj = new ArrayList[n+1];
    	visited = new boolean[n+1];
    	for(int i = 1; i <= n; i++)
			adj[i] = new ArrayList();
    }
	// print string "s" multiple times 
	// prefer to use this function for multiple printing
	public static String mp(String s, int times) {
		return String.valueOf(new char[times]).replace("\0", s);
	}
	// take log with base 2
 	public static long log2(long k) {
 		return 63-Long.numberOfLeadingZeros(k);
 	}

 	// using lambda function for sorting
   	public static void lambdaSort() {
   		Arrays.sort(arr, (a, b) -> Double.compare(a[0], b[0]));
   	}
  	
  	// (n choose k) = (n/k) * ((n-1) choose (k-1))
  	public static long choose(long n, long k) {
 		return (k == 0) ? 1 : (n*choose(n-1, k-1))/k;
 	}

 	// just for keeping gcd function for other personal purposes
 	public static long gcd(long a, long b) {
 		return (a == 0) ? b : gcd(b%a, a);
 	}
 	
	public static long max(long... as) {
        long max = Long.MIN_VALUE;
        for (long a : as) max = Math.max(a, max);
        return max;
    }

    public static long min(int... as) {
        long min = Long.MAX_VALUE;
        for (long a : as) min = Math.min(a, min);
        return min;
    }
 	
    public static long modpow(long x, long n, long mod) {
    	if(n == 0) return 1%mod;
    	long u = modpow(x, n/2, mod);
    	u = (u*u)%mod;
    	if(n%2 == 1) u = (u*x)%mod;
    	return u;
    }
 	// ======================= binary search (lower and upper bound) =======================
	public static int lowerBound(long[] a, int x) {
		int lo = 0;
 		int hi = a.length-1;
 		int ans = -1;
 		while(lo <= hi) {
 			int mid = (lo+hi)/2;
 			if(x < a[mid]) {
 				hi = mid-1;
 			} else if(x > a[mid]) {
 				lo = mid+1;
 			} else if(lo != hi) {
 				 hi = mid-1; 		// for first occurrence
 				 ans = mid;
 			} else {
 				return mid;
 			}
 		}
 		return ans;
	}
	
	public static int upperBound(long[] a, long x) {
		int lo = 0;
		int hi = a.length-1;
		int ans = -1;
		while(lo <= hi) {
			int mid = (lo+hi)/2;
			if(x < a[mid]) {
				hi = mid-1;
			} else if(x > a[mid]) {
				lo = mid+1;
			} else if(lo != hi) {
				lo = mid+1;			// for last occurrence
				ans = mid;
			} else {
				return mid;
			}
		}
		return ans;
	}
	// ================================================================

	// ================== SEIVE OF ERATOSTHENES =======================
	// Complexity : O(N * log(log(N)))       ( almost O(N) )
	public static void generatePrimes() {
		// set.add(0);
		// set.add(1);
		Arrays.fill(set, true);
		set[0] = false;
		set[1] = false;
		for(int i = 2; i <= seive_size; i++) {
			if(set[i]) {
				for(long j = (long) i*i; j <= seive_size; j+=i) 
					set[(int)j] = false;
				primes.add(i);
			}
		}
	}
  
	public static boolean isPrime(long N) {
		if(N <= seive_size) return set[(int)N];
		for (int i = 0; i < (int)primes.size(); i++)
			if (N % primes.get(i) == 0) return false;
		return true;
	}
	// ===========================================================
  
 	// ================ Permutation of String ====================
 	public static void permute(String str) {
 		permute(str, 0, str.length()-1);
 	}
 	public static void permute(String str, int l, int r) 
    { 
        if (l == r) 
            System.out.println(str); 
        else
        { 
            for (int i = l; i <= r; i++) 
            { 
                str = swap(str,l,i); 
                permute(str, l+1, r); 
                str = swap(str,l,i); 
            } 
        } 
    }
	public static String swap(String a, int i, int j) 
    { 
        char temp; 
        char[] charArray = a.toCharArray(); 
        temp = charArray[i] ; 
        charArray[i] = charArray[j]; 
        charArray[j] = temp; 
        return String.valueOf(charArray); 
    } 
	// Union-find
	void makeSet(int parent[], int rank[]) {

		int i;
		for(i = 0; i < parent.length; i++) {
			parent[i] = i;
			rank[i] = 0;
		}
	}
	public static int find(int u, int parent[]) {

		if(parent[u] == u)	return u;

		int v = find(parent[u], parent);
		parent[u] = v;
		return v;

	}
	public static boolean connected(int u, int v, int[] parent) {
		return find(u, parent) == find(v, parent);
	}
	public static void Union(int u, int v, int rank[], int parent[]) {

		int x = find(u, parent);				//root of u
		int y = find(v, parent);				//root of v

		if(x == y)		return;
		if(rank[x] == rank[y]) {
			parent[y] = x;
			rank[x]++;
		}
		else if(rank[x] > rank[y]) {
			parent[y] = x;
		}
		else {
			parent[x] = y;
		}

	}
	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {while (st == null || !st.hasMoreElements()) {
			try {st = new StringTokenizer(br.readLine());}
			catch (IOException e) {e.printStackTrace();}}
		return st.nextToken();}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine(){String str = "";
		try {str = br.readLine();}
		catch (IOException e) {e.printStackTrace();}
		return str;}
		int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
	}

}