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.util.*;
import java.io.*;
import java.text.*;
import java.math.*;
import static java.lang.Integer.*;
import static java.lang.Double.*;
import java.lang.Math.*;

public class roads_not_only_in_berland {

	public static FastIO file = new FastIO();

	public static int ntc, ctc;
	public static final long MOD = 1000000007L; // 998244353L;
	public static final int N = 200005, dx[] = { 0, 1, 0, -1 }, dy[] = { 1, 0, -1, 0 };

	public void run() throws Exception {
		ntc = 1; // nextInt();
		for (ctc = 1; ctc <= ntc; ++ctc)
			solve();
		file.out.flush();
		file.out.close();
	}

	public static class DSU {
		int[] pset;
		int[] size;
		int numsets;

		public DSU(int size) {
			this.numsets = size;
			this.pset = new int[size];
			this.size = new int[size];
			for (int i = 0; i < size; i++)
				this.pset[i] = i;
			for (int i = 0; i < size; i++)
				this.size[i] = 1;
		}

		public int find_set(int i) {
			return pset[i] == i ? i : (pset[i] = find_set(pset[i]));
		}

		public void unify(int i, int j) {
			int a = find_set(i), b = find_set(j);
			if (a == b)
				return;
			numsets--;
			if (size[a] < size[b]) {
				pset[a] = b;
				size[b] += size[a];
			} else {
				pset[b] = a;
				size[a] += size[b];
			}
		}

		public boolean same_set(int i, int j) {
			return find_set(i) == find_set(j);
		}

		int size_set(int i) {
			return size[find_set(i)];
		}
	}

	public static void solve() {
		int n = nextInt();
		DSU d = new DSU(n);
		ArrayList<Pair<Integer, Integer>> unne = new ArrayList<>(), add = new ArrayList<>();
		for (int i = 0; i < n - 1; i++) {
			int u = nextInt() - 1, v = nextInt() - 1;
			if (d.same_set(u, v)) {
				unne.add(new Pair<Integer, Integer>(u + 1, v + 1));
			}
			d.unify(u, v);
		}

		for (int j = 1; j < n; j++) {
			if (!d.same_set(0, j)) {
				add.add(new Pair<Integer, Integer>(1, j + 1));
				d.unify(0, j);
			}
		}

	println(add.size());
		//System.out.println(add);
		for (int i = 0; i < add.size(); i++) {
			println(unne.get(i).fi + " " + unne.get(i).se + " " + add.get(i).fi + " " + add.get(i).se);
		}
	}

	public static long mod(long n, long mod) {
		return (n % mod + mod) % mod;
	}

	public static long pow(long n, long p, long mod) {
		long ret = 1L;
		while (p > 0) {
			if (p % 2 != 0L)
				ret = mod(ret * n, mod);
			n = mod(n * n, mod);
			p >>= 1L;
		}
		return ret;
	}

	public static long pow(long n, long p) {
		long ret = 1L;
		while (p > 0) {
			if (p % 2 != 0L)
				ret *= n;
			n *= n;
			p >>= 1L;
		}
		return ret;
	}

	public static long gcd(long x, long y) {
		while (x != 0) {
			long tmp = x;
			x = y % x;
			y = tmp;
		}
		return y;
	}

	public static long lcm(long x, long y) {
		return x / gcd(x, y) * y;
	}

	public static boolean isPrime(int n) {
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
		return true;
	}

	public static class Pair<A, B> implements Comparable {
		public A fi;
		public B se;

		public Pair(A fi, B se) {
			this.fi = fi;
			this.se = se;
		}

		@Override
		public boolean equals(Object o) {
			if (this == o)
				return true;
			if (o == null || getClass() != o.getClass())
				return false;
			Pair<?, ?> p = (Pair<?, ?>) o;
			if (!fi.equals(p.fi))
				return false;
			return se.equals(p.se);
		}

		@Override
		public int hashCode() {
			return 31 * fi.hashCode() + se.hashCode();
		}

		@Override
		public String toString() {
			return fi.toString() + " " + se.toString();
		}

		public static <A, B> Pair<A, B> of(A a, B b) {
			return new Pair<A, B>(a, b);
		}

		public int compareTo(Object o) {
			Pair<?, ?> p = (Pair<?, ?>) o;
			if (fi.equals(p.fi))
				return ((Comparable) se).compareTo(p.se);
			return ((Comparable) fi).compareTo(p.fi);
		}
	}

	public static String next() {
		return file.next();
	}

	public static int nextInt() {
		return file.nextInt();
	}

	public static long nextLong() {
		return file.nextLong();
	}

	public static double nextDouble() {
		return file.nextDouble();
	}

	public static String nextLine() {
		return file.nextLine();
	}

	public static void print(Object o) {
		file.out.print(o);
	}

	public static void println(Object o) {
		file.out.println(o);
	}

	public static void printf(String s, Object... o) {
		file.out.printf(s, o);
	}

	public static class FastIO {
		BufferedReader br;
		StringTokenizer st;
		PrintWriter out;

		public FastIO() {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		void print(Object o) {
			out.print(o);
		}

		void println(Object o) {
			out.println(o);
		}

		void printf(String s, Object... o) {
			out.printf(s, o);
		}
	}

	public static void main(String[] args) throws Exception {
		new roads_not_only_in_berland().run();
	}
}