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 R25D2_D {
    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader(System.in);
        int n = in.readInt();
        DisjointSets sets = new DisjointSets(n+1);
        for (int i = 1; i <= n; i++) {
            sets.makeSet(i);
        }
        LinkedList<String> old = new LinkedList<String>();
        LinkedList<String> res = new LinkedList<String>();
        for (int i = 0; i < n-1; i++) {
            int a = in.readInt();
            int b = in.readInt();
            if(sets.find(a)!=sets.find(b)){
                sets.union(a, b);
            }else
                old.add(a+" "+b);
        }
        int mainSet = sets.find(1);
        int c = 0;
        for (int i = 2; i <= n; i++) {
            if(sets.find(i)!=sets.find(mainSet)){
                res.add(" "+1+" "+i);
                sets.union(1, sets.find(i));
                c++;
            }
        }
        System.out.println(c);
        ListIterator<String> itr1 = old.listIterator();
        ListIterator<String> itr2 = res.listIterator();
        while(itr1.hasNext() && itr2.hasNext()) {
            System.out.println(itr1.next()+itr2.next());
        }
    }
}
class DisjointSets {
    // if the integer elements can be indexes in array map them.
    static int[] parent;
    static int[] rank;
    static int[] size;

    public DisjointSets(int n) {
        parent = new int[n];
        rank = new int[n];
        size = new int[n];
    }

    public static void makeSet(int x) {
        parent[x] = x;
        rank[x] = 0;
        size[x] = 1;
    }

    public static int find(int x) {
        if (x != parent[x])
            parent[x] = find(parent[x]);
        return parent[x];
    }

    static void union(int x, int y) {
        int px = find(x);
        int py = find(y);
        if (rank[px] > rank[py]) {
            parent[py] = px;
            size[px] += size[py];
        } else {
            parent[px] = py;
            size[py] += size[px];
        }
        if (rank[px] == rank[py])
            rank[py] = rank[py] + 1;
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1000];
    private int curChar, numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    private 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 readInt() {
        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 readLong() {
        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 String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

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

    private String readLine0() {
        StringBuffer buf = new StringBuffer();
        int c = read();
        while (c != '\n' && c != -1) {
            buf.appendCodePoint(c);
            c = read();
        }
        return buf.toString();
    }

    public String readLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines)
            return readLine();
        else
            return readLine0();
    }

    public char readCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public double readDouble() {
        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, readInt());
            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, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
}