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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Omar-Handouk
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, FastReader in, OutputWriter out) {
            int n = in.nextInt();
            Disjoint_Set set = new Disjoint_Set(n);

            //Target is to make One set only.
            ArrayList<Road> redundent = new ArrayList<>();

            for (int i = 1; i <= n - 1; ++i) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;

                if (!set.sameSet(a, b))
                    set.union(a, b);
                else {
                    redundent.add(new Road(a, b));
                }
            }

            if (set.getSetCount() == 1)
                out.println(0);
            else {
                int days = 0;
                StringBuilder build = new StringBuilder();
                while (set.getSetCount() != 1) {
                    Road road = redundent.remove(0);
                    for (int i = 0; i < n; ++i) {
                        //System.err.println(road.from + " " + i);
                        //System.err.println(set.sameSet(road.from, i));
                        if (!set.sameSet(road.from, i)) {
                            build.append((road.from + 1) + " " + (road.to + 1) + " " + (road.from + 1) + " " + (i + 1) + "\n");
                            set.union(road.from, i);
                            ++days;
                            break;
                        }
                    }
                }
                out.println(days);
                out.println(build);
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }

    static class Disjoint_Set {
        private int Parent[];
        private int setSize[];
        private int Rank[];
        private int setCount;

        public Disjoint_Set(int Members) {
            Parent = new int[Members];
            setSize = new int[Members];
            Rank = new int[Members];
            setCount = Members;
            initialize(Members);
        }

        private void initialize(int Members) {
            for (int i = 0; i < Members; ++i) {
                Parent[i] = i;
                setSize[i] = 1;
            }
        }

        public int findSet(int Member) {
            if (Member == Parent[Member])
                return Member;

            return Parent[Member] = findSet(Parent[Member]);
        }

        public boolean sameSet(int Member_1, int Member_2) {
            return findSet(Member_1) == findSet(Member_2);
        }

        public void union(int Member_1, int Member_2) {
            if (sameSet(Member_1, Member_2))
                return;

            setCount = setCount - 1;

            int Parent_1 = findSet(Member_1);
            int Parent_2 = findSet(Member_2);

            if (Rank[Parent_1] > Rank[Parent_2]) {
                Parent[Parent_2] = Parent_1;
                setSize[Parent_1] = setSize[Parent_1] + setSize[Parent_2];
            } else if (Rank[Parent_1] < Rank[Parent_2]) {
                Parent[Parent_1] = Parent_2;
                setSize[Parent_2] = setSize[Parent_2] + setSize[Parent_1];
            } else {
                Parent[Parent_2] = Parent_1;
                setSize[Parent_1] = setSize[Parent_1] + setSize[Parent_2];
                Rank[Parent_1] = Rank[Parent_1] + 1;
            }
        }

        public int getSetCount() {
            return setCount;
        }

    }

    static class Road {
        int from;
        int to;

        Road(int a, int b) {
            from = a;
            to = b;
        }

    }

    static class FastReader {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        public FastReader(InputStream stream) {
            bufferedReader = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException error) {
                    error.printStackTrace();
                }
            }

            return stringTokenizer.nextToken();
        }

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

    }
}