As you know, Bob's brother lives in Flatland. In Flatland there are n cities, connected by n - 1 two-way roads. The cities are numbered from 1 to n. You can get from one city to another moving along the roads.

The «Two Paths» company, where Bob's brother works, has won a tender to repair two paths in Flatland. A path is a sequence of different cities, connected sequentially by roads. The company is allowed to choose by itself the paths to repair. The only condition they have to meet is that the two paths shouldn't cross (i.e. shouldn't have common cities).

It is known that the profit, the «Two Paths» company will get, equals the product of the lengths of the two paths. Let's consider the length of each road equals 1, and the length of a path equals the amount of roads in it. Find the maximum possible profit for the company.

Input

The first line contains an integer n (2 ≤ n ≤ 200), where n is the amount of cities in the country. The following n - 1 lines contain the information about the roads. Each line contains a pair of numbers of the cities, connected by the road ai, bi (1 ≤ ai, bi ≤ n).

Output

Output the maximum possible profit.

Examples

Input

4
1 2
2 3
3 4


Output

1


Input

7
1 2
1 3
1 4
1 5
1 6
1 7


Output

0


Input

6
1 2
2 3
2 4
5 4
6 4


Output

4
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class _14D {

    static int n;
    static List<Integer>[] edges;
    static int[] one, two;
    static int root;
    static int ans = 0;

    static void dfs(int u, int parent) {
        one[u] = two[u] = 0;
        int preMax = 0;
        for (int v : edges[u])
            if (v != parent) {
                dfs(v, u);
                one[u] = Math.max(one[u], one[v] + 1);
                if (preMax > 0) two[u] = Math.max(two[u], (one[v] + 1) + preMax);

                preMax = Math.max(preMax, one[v] + 1);
            }
        two[u] = Math.max(two[u], one[u]);
    }

    static boolean[] visited;
    static void dfs1(int u, int parent, int onePathLen) {
        visited[u] = true;

        for (int i=0; i<n; i++)
            if (!visited[i]) ans = Math.max(ans, two[i] * onePathLen);

        for (int v : edges[u])
            if (v != parent) dfs1(v, u, onePathLen + 1);

        visited[u] = false;
    }

  @SuppressWarnings("unchecked")
  public static void main(String[] args) throws Exception {
    Reader.init(System.in);
    BufferedWriter cout = new BufferedWriter(new OutputStreamWriter(System.out));

        n = Reader.nextInt();
        edges = new List[n];
        for (int i=0; i<edges.length; i++) edges[i] = new ArrayList<>();
        for (int i=0; i<n-1; i++) {
            int u = Reader.nextInt() - 1;
            int v = Reader.nextInt() - 1;
            edges[u].add(v);
            edges[v].add(u);
        }

        for (root=0; root<n; root++) {
            one = new int[n];
            two = new int[n];
            visited = new boolean[n];
            Arrays.fill(one, -1);
            Arrays.fill(two, -1);
            dfs(root, -1);
            dfs1(root, -1, 0);

//          if (root == 0) {
//              System.out.println(Arrays.toString(one));
//              System.out.println(Arrays.toString(two));
//          }
        }

        System.out.printf("%d", ans);

    cout.close();
  }

  static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
    final U _1;
    final V _2;

    private Pair(U key, V val) {
      this._1 = key;
      this._2 = val;
    }

    public static <U extends Comparable<U>, V extends Comparable<V>> Pair<U, V> instanceOf(U _1, V _2) {
      return new Pair<U, V>(_1, _2);
    }

    @Override
    public String toString() {
      return _1 + " " + _2;
    }

    @Override
    public int hashCode() {
      int res = 17;
      res = res * 31 + _1.hashCode();
      res = res * 31 + _2.hashCode();
      return res;
    }

    @Override
    public int compareTo(Pair<U, V> that) {
      int res = this._1.compareTo(that._1);
      if (res < 0 || res > 0)
        return res;
      else
        return this._2.compareTo(that._2);
    }

    @Override
    public boolean equals(Object obj) {
      if (this == obj)
        return true;
      if (!(obj instanceof Pair))
        return false;
      Pair<?, ?> that = (Pair<?, ?>) obj;
      return _1.equals(that._1) && _2.equals(that._2);
    }
  }

  /** Class for buffered reading int and double values */
  static class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
      reader = new BufferedReader(new InputStreamReader(input));
      tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
      while (!tokenizer.hasMoreTokens()) {
        // TODO add check for eof if necessary
        tokenizer = new StringTokenizer(reader.readLine());
      }
      return tokenizer.nextToken();
    }

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

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

  static class ArrayUtil {
    static void swap(int[] a, int i, int j) {
      int tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(long[] a, int i, int j) {
      long tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(double[] a, int i, int j) {
      double tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(char[] a, int i, int j) {
      char tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(boolean[] a, int i, int j) {
      boolean tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void reverse(int[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(long[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(double[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(char[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(boolean[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static long sum(int[] a) {
      int sum = 0;
      for (int i : a)
        sum += i;
      return sum;
    }

    static long sum(long[] a) {
      long sum = 0;
      for (long i : a)
        sum += i;
      return sum;
    }

    static double sum(double[] a) {
      double sum = 0;
      for (double i : a)
        sum += i;
      return sum;
    }

    static int max(int[] a) {
      int max = Integer.MIN_VALUE;
      for (int i : a)
        if (i > max)
          max = i;
      return max;
    }

    static int min(int[] a) {
      int min = Integer.MAX_VALUE;
      for (int i : a)
        if (i < min)
          min = i;
      return min;
    }

    static long max(long[] a) {
      long max = Long.MIN_VALUE;
      for (long i : a)
        if (i > max)
          max = i;
      return max;
    }

    static long min(long[] a) {
      long min = Long.MAX_VALUE;
      for (long i : a)
        if (i < min)
          min = i;
      return min;
    }
  }
}
