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.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Objects;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

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

    static class DRoadsNotOnlyInBerland {
        public void solve(int testNumber, InputReader c, OutputWriter w) {
            int n = c.readInt();
            UnionFind dsu = new UnionFind(n);
            ArrayList<Pair<Integer, Integer>> aa = new ArrayList<>();
            for (int i = 0; i < n - 1; i++) {
                int u = c.readInt() - 1, v = c.readInt() - 1;
                if (dsu.connected(u, v)) {
                    aa.add(new Pair<>(u, v));
                } else {
                    dsu.unify(u, v);
                }
            }

            w.printLine(aa.size());
            ArrayList<Integer> comp = new ArrayList<>();
            HashSet<Integer> hh = new HashSet<>();
            for (int i = 0; i < n; i++) {
                if (!hh.contains(dsu.find(i))) {
                    hh.add(dsu.find(i));
                    comp.add(dsu.find(i));
                }
            }

            for (int i = 0; i < comp.size() - 1; i++) {
                w.printLine(aa.get(i).first + 1, aa.get(i).second + 1, comp.get(i) + 1, comp.get(comp.size() - 1) + 1);
            }


        }

    }

    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 printLine(Object... objects) {
            print(objects);
            writer.println();
        }

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

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

    }

    static class UnionFind {
        private int size;
        private int[] sz;
        private int[] id;
        private int numComponents;

        public UnionFind(int size) {

            if (size <= 0) {
                throw new IllegalArgumentException("Size <= 0 is not allowed");
            }

            this.size = numComponents = size;
            sz = new int[size];
            id = new int[size];

            for (int i = 0; i < size; i++) {
                id[i] = i;
                sz[i] = 1;
            }
        }

        public int find(int p) {

            int root = p;
            while (root != id[root]) {
                root = id[root];
            }

            while (p != root) {
                int next = id[p];
                id[p] = root;
                p = next;
            }

            return root;
        }

        public boolean connected(int p, int q) {
            return find(p) == find(q);
        }

        public void unify(int p, int q) {

            int root1 = find(p);
            int root2 = find(q);

            if (root1 == root2) {
                return;
            }

            if (sz[root1] < sz[root2]) {
                sz[root2] += sz[root1];
                id[root1] = root2;
            } else {
                sz[root1] += sz[root2];
                id[root2] = root1;
            }
            numComponents--;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        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 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 boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

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

        }

    }

    static class Pair<U, V> implements Comparable<Pair<U, V>> {
        public final U first;
        public final V second;

        public Pair(U first, V second) {
            this.first = first;
            this.second = second;
        }

        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return first.equals(pair.first) &&
                    second.equals(pair.second);
        }

        public int hashCode() {
            return Objects.hash(first, second);
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(Pair<U, V> o) {
            int value = ((Comparable<U>) first).compareTo(o.first);
            if (value != 0) {
                return value;
            }
            return ((Comparable<V>) second).compareTo(o.second);
        }

    }
}