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.*;
import java.util.*;

public class MinimalDiameterForest implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        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 long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new MinimalDiameterForest(),"Main",1<<26).start();
    }

    static long gcd(long a,long b){ if(b==0)return a;return gcd(b,a%b); }
    static long modPow(long a,long p,long m){ if(a==1)return 1;long ans=1;while (p>0){ if(p%2==1)ans=(ans*a)%m;a=(a*a)%m;p>>=1; }return ans; }
    static long modInv(long a,long m){return modPow(a,m-2,m);}


    ArrayList<Integer> l[];
    int dist[],parent[];

    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n=sc.nextInt();
        int m=sc.nextInt();
        l=new ArrayList[n+1];
        for (int i = 1; i <n+1 ; i++) {
            l[i]=new ArrayList<>();
        }
        for (int i = 0; i <m ; i++) {
            int u=sc.nextInt();
            int v=sc.nextInt();
            l[u].add(v);
            l[v].add(u);
        }
        dist=new int[n+1];
        parent=new int[n+1];

        Arrays.fill(dist,-1);

        ArrayList<Node> lt=new ArrayList<>();

        for (int i = 1; i <= n; i++) {
            if(dist[i]==-1){
                lt.add(find_root(i));
            }
        }

        Collections.sort(lt, new Comparator<Node>() {
            @Override
            public int compare(Node o1, Node o2) {
                return Integer.compare(o1.d,o2.d);
            }
        });

        int maxx=lt.get(lt.size()-1).d;
        if(lt.size()>1){
            maxx=Math.max(maxx,(lt.get(lt.size()-2).d+1)/2+(maxx+1)/2 +1);
            if(lt.size()>2){
                maxx=Math.max(maxx,(lt.get(lt.size()-2).d+1)/2+(lt.get(lt.size()-3).d+1)/2+2);
            }
        }
        out.println(maxx);
        for (int i = 0; i <lt.size()-1 ; i++) {
            out.println(lt.get(i).root+" "+lt.get(lt.size()-1).root);
        }

        out.close();
    }

    int max;
    private Node find_root(int i) {
        dist[i]=0;
        max=i;
        dfs(i,0);
        dist[max]=0;
        dfs(max,0);
        int temp=dist[max];
        for (int j = 0; j <temp/2 ; j++) {
            max=parent[max];
        }
        return new Node(max,temp);
    }

    void dfs(int u,int par){
        parent[u]=par;
        for(int v:l[u]){
            if(v==par)continue;
            dist[v]=dist[u]+1;
            if(dist[v]>dist[max]){
                max=v;
            }
            dfs(v,u);
        }
    }


    class Node{
        int root,d;

        public Node(int root, int d) {
            this.root = root;
            this.d = d;
        }
    }
}