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.*;
import java.lang.InternalError;

public class Main {
    static PrintWriter pw;
    static Scanner sc;
    static long[][] dp;
    static int mod, arr[][];
    static ArrayList<Integer> ans;
    static int[] fact;
    static long ceildiv(long x, long y) { return (x + y - 1) / y; }
    static int mod(long x, int m) { return (int) ((x % m + m) % m); }
    public static long gcd(long x, long y) {return y==0?x:gcd(y, x%y);}
    public static void main(String[] args) throws Exception {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        int n=sc.nextInt();
        Union dsu=new Union(n);
        for(int i=1; i<n; i++){
            int x=sc.nextInt()-1, y=sc.nextInt()-1;
            dsu.join(x, y);
        }
        HashSet<Integer> hash=new HashSet<>();
        for(int i=0; i<n; i++){
            int x=dsu.getSet(i);
            if(!hash.contains(x))
                hash.add(x);
        }
        int[] arr=new int[hash.size()];
        int i=0;
        for(int x: hash)
            arr[i++]=x;
        pw.println(arr.length-1);
        for(i=1; i<arr.length; i++)
            dsu.replace(arr[i-1]+1, arr[i]+1);
        pw.close();
    }
    static int modInv(int x, int mod){
        return Euclid(x, mod).x;
    }
    static Pair Euclid(int x, int y){
        if(y==0)
            return new Pair(1, 0);
        Pair p=Euclid(y, x%y);
        int a=p.y, b=(int)(p.x-p.y*1l*(x/y));
        return new Pair(a, b);
    }
    static long C(int n, int r, int mod){
        return (fact[n]*1l*mod(modInv((int)((fact[n-r]*1l*fact[r])%mod), mod), mod))%mod;
    }
    static void printArr(int[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            pw.print(arr[i] + " ");
        pw.println(arr[arr.length - 1]);
    }
    static void printArr(long[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            pw.print(arr[i] + " ");
        pw.println(arr[arr.length - 1]);
    }
    static void printArr(Integer[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(char[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i]==0? '1': arr[i]);
        pw.println();
    }
    static void printArr(ArrayList<Integer> list) {
        for (int i = 0; i < list.size(); i++)
            pw.print(list.get(i)+1+" ");
        pw.println();
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public int[] nextArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < arr.length; i++)
                arr[i] = nextInt();
            return arr;
        }
        public Integer[] nextsort(int n) throws IOException{
            Integer[] arr=new Integer[n];
            for(int i=0; i<n; i++)
                arr[i]=nextInt();
            return arr;
        }
        public Pair nextPair() throws IOException{
            return new Pair(nextInt(), nextInt());
        }
        public Pair[] nextPairArr(int n) throws IOException{
            Pair[] arr=new Pair[n];
            for(int i=0; i<n; i++)
                arr[i]=new Pair(nextInt(), nextInt());
            return arr;
        }
        public boolean ready() throws IOException {
            return br.ready();
        }
    }
    static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
        public int hashCode() {
            return (this.x*1000+this.y);
        }
        public int compareTo(Pair p){
            return Long.compare(this.x, p.x);
        }
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (this.getClass() != obj.getClass()) {
                return false;
            }
            Pair p = (Pair) obj;
            return this.x==p.x && this.y==p.y;
        }
        public boolean equal(Pair p){
            if(this.x==p.x)
                return this.y==p.y;
            if(this.x==p.y)
                return this.y==p.x;
            else
                return false;
        }
        public Pair clone(){
            return new Pair(x, y);
        }
        public String toString(){
            return this.x+" "+this.y;
        }
        public void add(Pair p){
            x+=p.x;
            y+=p.y;
        }
    }
    static class Union{
        int[] rep, size;
        HashSet<Pair> useless;
        public Union(int n){
            rep=new int[n];
            size=new int[n];
            for(int i=0; i<n; i++){
                rep[i]=i;
                size[i]=1;
            }
            useless=new HashSet<Pair>();
        }
        public void join(int x, int y){
            int a=getSet(x), b=getSet(y);
            if(a==b){
                useless.add(new Pair(x, y));
                return;
            }
            if(size[a]>size[b]){
                rep[b]=a;
                size[a]+=size[b];
            }else{
                rep[a]=b;
                size[b]+=size[a];
            }
        }
        public void replace(int x, int y){
            Pair use=new Pair(0, 0);
            for(Pair p: useless){
                use=new Pair(p.x+1, p.y+1);
                break;
            }
            useless.remove(new Pair(use.x-1, use.y-1));
            pw.print(use+" ");
            pw.println(x+" "+y);
        }
        public int getSet(int x){
            if(rep[x]==x)
                return x;
            return rep[x]=getSet(rep[x]);
        }
    }
}