Problem: Berland Government decided to improve relations with neighboring countries. First of all, it was decided to build new roads so that from each city of Berland and neighboring countries it became possible to reach all the others. There are n cities in Berland and neighboring countries in total and exactly n - 1 two-way roads. Because of the recent financial crisis, the Berland Government is strongly pressed for money, so to build a new road it has to close some of the existing ones. Every day it is possible to close one existing road and immediately build a new one. Your task is to determine how many days would be needed to rebuild roads so that from each city it became possible to reach all the others, and to draw a plan of closure of old roads and building of new ones.

Input

The first line contains integer n (2 ≤ n ≤ 1000) — amount of cities in Berland and neighboring countries. Next n - 1 lines contain the description of roads. Each road is described by two space-separated integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — pair of cities, which the road connects. It can't be more than one road between a pair of cities. No road connects the city with itself.

Output

Output the answer, number t — what is the least amount of days needed to rebuild roads so that from each city it became possible to reach all the others. Then output t lines — the plan of closure of old roads and building of new ones. Each line should describe one day in the format i j u v — it means that road between cities i and j became closed and a new road between cities u and v is built. Cities are numbered from 1. If the answer is not unique, output any.

Examples

Input

2
1 2


Output

0


Input

7
1 2
2 3
3 1
4 5
5 6
6 7


Output

1
3 1 3 7

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class working
{
    static PrintWriter out=new PrintWriter((System.out));
    static ArrayList<Integer>[] adj;
    static ArrayList<Integer> ans=new ArrayList<>();
    static int[] init,goal;
    public static void main(String args[])throws IOException
    {
        Reader sc=new Reader();
        
        int n=sc.nextInt();
        // adj=new ArrayList[n+1];
        // for(int i=0;i<=n;i++) adj[i]=new ArrayList<>();
        int[] par=new int[n+1];
        int[] rank=new int[n+1];
        for(int i=1;i<=n;i++) make_set(i,par,rank);
        ArrayList<int[]> del=new ArrayList<>();
        ArrayList<int[]> merge=new ArrayList<>();
        for(int tt=0;tt<n-1;tt++){
            int x=sc.nextInt(),y=sc.nextInt();
            // adj[x].add(y);
            // adj[y].add(x);
            if(find_set(x,par)==find_set(y, par)){
                del.add(new int[]{x,y});
            }
            else union_set(x, y, par, rank);
        }
        // comp
        for(int i=2;i<=n;i++){
            if(find_set(i, par)!=find_set(1, par)){
                union_set(i, 1, par, rank);
                merge.add(new int[]{1,i});
            }
        }
        out.println(del.size());
        for(int i=0;i<del.size();i++){
            out.print(del.get(i)[0]+" "+del.get(i)[1]+" ");
            out.println(merge.get(i)[0]+" "+merge.get(i)[1]);
        }       

        out.close();
    }
    // dsu
    
    private static void make_set(int v,int[] par,int[] rank){
        par[v]=v;
        rank[v]=0;
    }
    private static int find_set(int x,int[] par){
        if(par[x]==x) return x;
        return par[x]=find_set(par[x],par);
    }
    private static void union_set(int x,int y,int[] par,int[] rank){
        x=find_set(x,par);
        y=find_set(y,par);
        if(x==y) return;
        if(rank[x]<rank[y]){
            int tmp=x;
            x=y;
            y=tmp;
        }
        par[y]=x;
        if(rank[x]==rank[y]){
            rank[x]++;
        }
    }
    
    private static int dfs(int i,int par,int even_count,int odd_count,int level){
        int res=0;
        int curr;
        if(level%2==0){
            curr=(init[i]+even_count)%2;
            if(curr!=goal[i]){
                even_count++;
                res++;
                ans.add(i);
            }
        }else{
            curr=(init[i]+odd_count)%2;
            if(curr!=goal[i]){
                odd_count++;
                res++;
                ans.add(i);
            }
        }
        
        for(int j:adj[i]){
            if(j==par) continue;
            res+=dfs(j,i,even_count,odd_count,level+1);
        }
        return res;
    }
    
    // private static void dfs(ArrayList<Integer>[] adj,int i,int par,boolean[] vis){
    //     for(int j:adj[i]){
    //         if(j!=par){
    //             vis[j]=true;
    //             dfs(adj,j,i,vis);
    //         }
    //     }
    // }

    // private static boolean possible(char[][] grid,int i,int j){
    //     return (i>=0 && j>=0 && i<grid.length && j<grid[0].length);
    // }
    /*
    int n=sc.nextInt();
        	char[] s=sc.next().toCharArray();
        	int res=0;
        	for(int i=1;i<n;i++){
        		if( (s[i]=='1') && s[i]==s[i-1]) res++;
        	}
        	out.println(res);
    
    private static int modInverse(int a, int m) 
    { 
        a = a % m; 
        for (int x = 1; x < m; x++) 
           if ((a * x) % m == 1) 
              return x; 
        return 1;  
   }
    
    private static int gcd(int a,int b){
    	if(b==0) return a;
    	return gcd(b,a%b);
    }
    
    private static int dfs(ArrayList<Integer>[] adj,int[] arr,int i,int par){
    	if(adj[i].size()==0) return arr[i];
    	int curr=arr[i],s=adj[i].size();
    	int max=0;
        for(int j:adj[i]){
        	if(j==par) continue;
        	int temp=dfs(adj,arr,j,i);
        	max=Math.max(max,temp);
        	curr+=temp;
        }
        int rem=curr%s;
        if(rem>0) rem=1;
        int ans=rem+curr/s;
        if(max>ans) return max;
        return ans;
    }
     */
    public static long pow(long a,long b){
        if(b==0){
            return 1;
        }
        if(b%2==0){
            return pow(a*a,b/2);
        }else{
            return a*pow(a*a,b/2);
        }
    }
    static class Reader 
    { 
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next()
        {
            while(!st.hasMoreTokens())
            {
                try
                {
                    st=new StringTokenizer(br.readLine());
                }
                catch(Exception e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        public int nextInt()
        {
            return Integer.parseInt(next());
        }
        public long nextLong()
        {
            return Long.parseLong(next());
        }
        public double nextDouble()
        {
            return Double.parseDouble(next());
        }
        public String nextLine()
        {
            try
            {
                return br.readLine();
            }
            catch(Exception e)
            {
                e.printStackTrace();
            }
            return null;
        }
        public boolean hasNext()
        {
            String next=null;
            try
            {
                next=br.readLine();
            }
            catch(Exception e)
            {
            }
            if(next==null)
            {
                return false;
            }
            st=new StringTokenizer(next);
            return true;
        }
    } 
}