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.util.Iterator;
import java.io.BufferedWriter;
import java.util.Set;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
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);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskD {
		int[] dsu;
		Set<Integer> groups;

		public void solve(int testNumber, InputReader in, OutputWriter out) {
			int n = in.readInt();
			List<IntPair> roadsToRemove = new ArrayList<>(n);
			dsu = new int[n];
			dsuInit();
			for (int i = 0; i < n - 1; i++) {
				int from = in.readInt() - 1;
				int to = in.readInt() - 1;
				if (!tryUnite(from, to))
					roadsToRemove.add(new IntPair(from, to));
			}

			out.printLine(roadsToRemove.size());
			roadsToRemove.forEach(road -> {
				int from = road.first;
				int to = road.second;

				int newFrom = from;
				int newTo;
				Iterator<Integer> iter = groups.iterator();
				if ((newTo = iter.next()) == dsuFindSet(newFrom))
					newTo = iter.next();
				tryUnite(newFrom, newTo);

				out.printFormat("%d %d %d %d\n", ++from, ++to, ++newFrom, ++newTo);
			});
		}

		boolean tryUnite(int i, int j) {
			int p1 = dsuFindSet(i);
			int p2 = dsuFindSet(j);

			if (p1 != p2) {
				dsu[p2] = p1;
				groups.remove(p2);
				return true;
			} else {
				return false;
			}
		}

		int dsuFindSet(int i) {
			if (dsu[i] == i) return i;
			return dsu[i] = dsuFindSet(dsu[i]);
		}

		void dsuInit() {
			groups = new HashSet<>(dsu.length);
			for (int i = 0; i < dsu.length; i++)
				groups.add(dsu[i] = i);
		}

	}

	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 printFormat(String format, Object... objects) {
			writer.printf(format, objects);
		}

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

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

	}

	static class IntPair implements Comparable<IntPair> {
		public final int first;
		public final int second;

		public IntPair(int first, int second) {
			this.first = first;
			this.second = second;
		}


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


		public boolean equals(Object o) {
			if (this == o) return true;
			if (o == null || getClass() != o.getClass()) return false;

			IntPair intPair = (IntPair) o;

			return first == intPair.first && second == intPair.second;

		}


		public int hashCode() {
			int result = first;
			result = 31 * result + second;
			return result;
		}

		public int compareTo(IntPair o) {
			if (first < o.first)
				return -1;
			if (first > o.first)
				return 1;
			if (second < o.second)
				return -1;
			if (second > o.second)
				return 1;
			return 0;
		}

	}

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

		}

	}
}