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.awt.List;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.Reader;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.Iterator;
import java.util.StringTokenizer;
import java.util.Vector;


public class trip {

	/**
	 * @param args
	 * @throws IOException 
	 * @throws NumberFormatException 
	 */
	
	
	
	class Pair{
		public Pair(int x, int v) {
			// TODO Auto-generated constructor stub
			first = x;
			second = v;
		}

		int first, second;
		
		@Override
		public String toString() {
			// TODO Auto-generated method stub
			return first + " " + second + "";
		}
	}
	
	class SNM{
		private ArrayList<Integer> a;
		
		public SNM(int n){
			a = new ArrayList<Integer>(n);
			for (int i = 0; i < n; ++ i)
				a.add(new Integer(i));
		}
		
		public int p(int n){
			if (a.get(n) == n)
				return n;
			a.set(n, p(a.get(n)));
			return a.get(n);
		}
		
		public void Union(int first, int second) {
			if (Math.random() % 2 == 0)
				a.set(p(first), p(second));
			else
				a.set(p(second), p(first));
		}
		
		public boolean one(int first, int second){
			return p(first) == p(second);
		}
	}
	
	ArrayList<Boolean> was;
	ArrayList<Boolean> used;
	ArrayList<Integer> g[];
	
	void dfs(int x, int p, ArrayList<Pair> a){
		if (used.get(x))
			return;
		used.set(x, new Boolean(true));
		
		for (Integer v : g[x]){
			if (v.intValue() != p && used.get(v) && !was.get(v))
				a.add(new Pair(x, v));
			else
				dfs(v, x, a);
		}
		was.set(x, new Boolean(true));
	}
	
	private void solve() throws IOException{
		
		int n = nextInt();
		
		g = new ArrayList[n];
		
		for (int i = 0; i < n; ++ i)
			g[i] = new ArrayList<Integer>();
			
		SNM s = new SNM(n);
		for (int i = 0; i < n - 1; ++ i){
			int l = nextInt() - 1;
			int r = nextInt() - 1;
			g[l].add(r);
			g[r].add(l);
			s.Union(l, r);
		}
		
		ArrayList<Pair> a = new ArrayList<Pair>();
		
		was = new ArrayList<Boolean>();
		used = new ArrayList<Boolean>();
		
		for (int i = 0; i < n; ++ i){
			was.add(new Boolean(false));
			used.add(new Boolean(false));
		}
		
		for (int i = 0; i < n; ++ i){
			if (!was.get(i))
				dfs(i, -1, a);
		}
		
		out.print(a.size() + "\n");
		//out.print(a.toString());
		
		
		for (Pair v : a){
			for (int i = 1; i < n; ++ i){
				if (!s.one(0, i)){
					s.Union(0, i);
					out.print((v.first + 1) + " " + (v.second + 1) + " 1 " + (i + 1) + "\n" );
					break;
				}
			}
		}
		
	}
	
	
	
	StringTokenizer in;
	BufferedReader reader;
	PrintWriter out;
	
	double nextDouble() throws IOException{
		return Double.parseDouble(nextTokinazer());
	}
	
	long nextLong() throws  IOException{
		return Long.parseLong(nextTokinazer());
	}
	
	int nextInt() throws  IOException{
		return Integer.parseInt(nextTokinazer());
	}
	
	private String nextTokinazer() throws IOException{
		while (in == null || !in.hasMoreElements())
			in = new StringTokenizer(reader.readLine());
		return in.nextToken();
	}
	
	void run() throws IOException{
		in = null;
		reader = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
	}
	
	
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub

		new trip().run();
	}

}