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 DSUBerland
{
    static int parent[] = new int[1001];
    static int size [] = new int [1001];
    public static void main(String[]args)
    {
        InputReader1 sc = new InputReader1(System.in);
        int N = sc.nextInt();
        for(int i=1;i<=N;i++)
        {
            parent [i] = i;
            size[i] = 1;
        }
        ArrayList<Pair> rem = new ArrayList<Pair>();
        ArrayList<Pair> ins = new ArrayList<Pair>();
        for(int i=1;i<N;i++)
        {
            int u = sc.nextInt();
            int v = sc.nextInt();
            if(find(u) == find(v))
                rem.add(new Pair(u,v));
            else
                union(u,v);
        }
        
        for(int i=1;i<=N;i++)
        {
            for(int j=i+1;j<=N;j++)
            {
                if(find(i)!=find(j))
                {
                    ins.add(new Pair(i,j));
                    union(i,j);
                }
            }
        }
        System.out.println(ins.size());
        for(int i=0;i<ins.size();i++)
        System.out.println(rem.get(i).first+" "+rem.get(i).second+" "+ins.get(i).first+" "+ins.get(i).second);     
    }
    static int find(int x)
    {
        if(parent[x]==x)return x;
        else return parent[x] = find(parent[x]);
    }
    static void union(int i , int j)
    {
        int u = find(i);
        int v = find(j);
        if(u==v)return;
        if(size[u] < size[v])
        {
            size[v] += size[u];
            parent[u]=v;
        }
        else
        {
            size[u]+=size[v];
            parent[v]=u;
        }
    }
}
class Pair
{
    int first , second;
    public Pair(int first ,int second)
    {
        this.first = first;
        this.second = second;
    }
}
class InputReader1 
{

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader1(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 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 & 15;
            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 & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String next() {
        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 String nextLine() {
        int c = read();
        //while (c != '\n' && c != '\r' && c != '\t' && c != -1)
        //c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (c != '\n' && c != '\r' && c != '\t' && c != -1);
        return res.toString();
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}