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.util.*;

import java.io.*;
import java.lang.*;
import java.math.*;

public class D_25 implements Runnable{
    static class UnionFind{
        int size[] ;
        int parent[];
        int noOfComponents;
    
        public int getSize(int n){
            return size[find(n)];
        }
    
        public boolean isConnected(int a,int b){
            return find(a)==find(b);
        }
    
        public UnionFind(int s){
            size = new  int[s];
            parent = new int[s];
            noOfComponents = s;
            for(int i = 0;i<s;i++){
                parent[i] = i;
            }
            Arrays.fill(size,1);
        }
    
        public int getNumberOfComponents(){
            return noOfComponents;
        }
    
        public void union(int a,int b){
            int root1 = find(a);
            int root2 = find(b);
            if(root1==root2) return;
            parent[root1] = parent[root2];
            
            noOfComponents--;
        }
    
        public int find(int a){
            int temp = a;
            while(temp!=parent[temp]){
                // size[temp]+=1;
                temp = parent[temp];
            }
            while(a!=temp){
                int k = parent[a];
                parent[a] = temp;
                a = k;
            }
            return temp;
        }
    
        void print(){
            for(int i = 0;i<parent.length;i++){
                System.out.println(i+" "+parent[i]);
            }
            return ;
        }
    
        public static void main(String[] args) {
            Scanner scan = new Scanner(System.in);
            int n = scan.nextInt();
            int m = scan.nextInt();
            UnionFind uf = new UnionFind(n);
            for(int i = 0;i<m;i++){
                int u = scan.nextInt()-1;
                int v = scan.nextInt()-1;
                uf.union(u,v);
            }
            for(int i = 0;i<n;i++){
                System.out.print(uf.getSize(i)-1+" ");
            }
            System.out.println(Arrays.toString(uf.parent));
        }
    
    }
        

    static class Pair{
        int a,b;
        Pair(int aa,int bb){
            a =aa;
            b =bb;
        }
    }

    public void solve(){
        int n= scan.nextInt();
        UnionFind uf = new UnionFind(n);
        List<Pair> l = new ArrayList<>();
        for(int i=1;i<n;i++){
            int a = scan.nextInt();
            int b = scan.nextInt();
            a--;b--;
            if(!uf.isConnected(a, b))
            uf.union(a,b);
            else l.add(new Pair(a,b));
        }
        System.out.println(l.size());
        StringBuilder sb = new StringBuilder();
        for(Pair pp : l){
            int k = uf.find(pp.a);
            sb.append((1+pp.a)+ " "+(1+pp.b)+ " ");
            for(int i = 0;i<n;i++){
                if(uf.parent[i]==i && i!=k){
                    uf.union(i,k);
                    sb.append((1+i)+ " "+(1+k));
                    break;
                }
            }
            sb.append("\n");
        } 
        System.out.print(sb.toString());

    }
    
    InputReader scan;
    PrintWriter out;
    
    @Override
    public void run(){
        scan = new InputReader(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.flush();
        out.close();
    }
    
    public static void main(String[] args) {
        new Thread(null,new D_25(),"Main",1<<26).start();
    }
    
    
    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 long[] nla(int n){ //nextLongArray()
            long ar[] = new long[n];
            for(int i=0;i<n;i++){
                ar[i] = this.nextLong();
            }
            return ar;
        }

        public int[] nia(int n){
            int ar[] = new int[n];
            for(int i=0;i<n;i++){
                ar[i] = this.nextInt();
            }
            return ar;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

}