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 static java.lang.Math.*;
import static java.util.Arrays.*;
import java.util.*;
import java.io.*;

public class Main {
	public static void main(String[] args) throws Exception {
		Class<?> here = new Object(){}.getClass().getEnclosingClass();
		try {
			String packageName = here.getPackage().getName();
			packageName = "src/" + packageName.replaceAll("\\.", "/") + "/";
			System.setIn(new FileInputStream(packageName + "input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream(packageName + "output.txt")));
		} catch (FileNotFoundException e) {
		} catch (NullPointerException e) {
		}

		Object o = Class.forName(here.getName()).newInstance();
		o.getClass().getMethod("run").invoke(o);
	}

	static void tr(Object... os) {
		System.err.println(deepToString(os));
	}
	class UnionFind {
		int[] data;

		public UnionFind(int n) {
			data = new int[n];
			fill(data, -1);
		}

		boolean link(int x, int y) {
			x = root(x);
			y = root(y);
			if (x != y) {
				if (data[y] < data[x]) {
					data[y] += data[x];
					data[x] = y;
				} else {
					data[x] += data[y];
					data[y] = x;
				}
			}
			return x != y;
		}

		int root(int x) {
			return data[x] < 0 ? x : (data[x] = root(data[x]));
		}

		int size(int x) { // 要素xが含まれる集合の大きさ
			return -data[root(x)];
		}

		boolean same(int x, int y) { // 同じ集合ならtrue
			return root(x) == root(y);
		}

		int num() { // 異なる集合の数
			int res = 0;
			for (int i = 0; i < data.length; i++)
				res += (root(i) == i) ? 1 : 0;
			return res;
		}
	}

	MyScanner sc = null;
	PrintWriter out = null;
	public void run() throws Exception {
		sc = new MyScanner(System.in);
		out = new PrintWriter(System.out);
		for (;sc.hasNext();) {
			solve();
			out.flush();
		}
		out.close();
	}

	void solve() {
		int n = sc.nextInt();

		UnionFind uf = new UnionFind(1000);
		List<Integer> waste = new LinkedList<Integer>();

		for (int i = 0; i < n - 1; i++) {
			int a = sc.nextInt() - 1;
			int b = sc.nextInt() - 1;
			if (uf.same(a, b)) {
				waste.add(a+1);
				waste.add(b+1);
			} else {
				uf.link(a, b);
			}
		}

		out.println(waste.size() / 2);
		int p = 0;
		for (int i = 1; i < n; i++) if (!uf.same(0, i)) {
			uf.link(0, i);
			out.println(waste.get(p++) + " " + waste.get(p++) + " " + 1 + " " + (i + 1));
		}
	}


	void print(int[] a) {
		out.print(a[0]);
		for (int i = 1; i < a.length; i++) out.print(" " + a[i]);
		out.println();
	}

	class MyScanner {
		String line;
		BufferedReader reader;
		StringTokenizer tokenizer;

		public MyScanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}

		public void eat() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					line = reader.readLine();
					if (line == null) {
						tokenizer = null;
						return;
					}
					tokenizer = new StringTokenizer(line);
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}

		public String next() {
			eat();
			return tokenizer.nextToken();
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

		public boolean hasNext() {
			eat();
			return (tokenizer != null && tokenizer.hasMoreElements());
		}

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

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

		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0;i < n;i++) a[i] = nextInt();
			return a;
		}
	}
}