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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.min;

public class BerlandDsu {
    static class Task {
        int n;
        List<Integer>[] adj;
        int[] state;
        List<int[]> ans;
        int[] link;
        int[] sz;

        void init() {
            link = new int[n + 1];
            Arrays.setAll(link, i -> i);
            sz = new int[n + 1];
            Arrays.fill(sz, 1);
        }

        int find(int u) {
            while (u != link[u]) {
                u = link[u];
            }
            return u;
        }

        boolean same(int u, int v) {
            return find(u) == find(v);
        }

        void unite(int u, int v) {
            u = find(u);
            v = find(v);
            assert (u != v);
            if (sz[u] > sz[v]) {
                int temp = u;
                u = v;
                v = temp;
            }
            link[u] = v;
            sz[v] += sz[u];
        }

        void dfs(int u, int par) {
            state[u] = 1;
            for (int v : adj[u]) {
                if (v == par) {
                    continue;
                }
                if (state[v] == 1) {
                    // found cycle
                    for (int i = 1; i <= n; i++) {
                        if (!same(u, i)) {
                            unite(u, i);
                            ans.add(new int[]{u, v, u, i});
                            break;
                        }
                    }
                } else if (state[v] == 0) {
                    dfs(v, u);
                }
            }
            state[u] = 2;
        }

        public void solve() {
            n = ni();
            adj = new List[n + 1];
            Arrays.setAll(adj, i -> new ArrayList<>());
            init();
            for (int it = 0; it < n - 1; it++) {
                int u = ni(), v = ni();
                adj[u].add(v);
                adj[v].add(u);
                if (!same(u, v)) {
                    unite(u, v);
                }
            }

            ans = new ArrayList<>();
            state = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                if (state[i] == 0) {
                    dfs(i, -1);
                }
            }

            out.println(ans.size());
            for (int[] a : ans) {
                for (int i = 0; i < 4; i++) {
                    out.print(a[i] + " ");
                }
                out.println();
            }
        }

    }


    /*==================================================================================================================*/

    // Startup
    static String INPUT = "";
    static PrintWriter out;

    public static void main(String[] args) {
        // is = new ByteArrayInputStream(INPUT.getBytes());
        is = System.in;
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        Task solver = new Task();
        int tt = 1;
        // tt = ni();
        for (int i = 1; i <= tt; i++) {
            solver.solve();
        }
        out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }


    // Input/output
    static InputStream is;
    private static final byte[] inbuf = new byte[1024];
    public static int lenbuf = 0, ptrbuf = 0;

    private static int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private static int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private static double nd() {
        return Double.parseDouble(ns());
    }

    private static char nc() {
        return (char) skip();
    }

    private static String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private static char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private static int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    // Debug
    private static final boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private static void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }
}