Problem:
Score : 200 points

Problem Statement

We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.

In how many ways can we choose three of the sticks with different lengths that can form a triangle?

That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:

L_i, L_j, and L_k are all different.

There exists a triangle whose sides have lengths L_i, L_j, and L_k.

Constraints

1 \leq N \leq 100

1 \leq L_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 \cdots L_N

Output

Print the number of ways to choose three of the sticks with different lengths that can form a triangle.

Sample Input 1

5
4 4 9 7 5

Sample Output 1

5

The following five triples (i, j, k) satisfy the conditions: (1, 3, 4), (1, 4, 5), (2, 3, 4), (2, 4, 5), and (3, 4, 5).

Sample Input 2

6
4 5 4 3 3 5

Sample Output 2

8

We have two sticks for each of the lengths 3, 4, and 5. To satisfy the first condition, we have to choose one from each length.

There is a triangle whose sides have lengths 3, 4, and 5, so we have 2 ^ 3 = 8 triples (i, j, k) that satisfy the conditions.

Sample Input 3

10
9 4 6 1 9 6 10 6 6 8

Sample Output 3

39

Sample Input 4

2
1 1

Sample Output 4

0

No triple (i, j, k) satisfies 1 \leq i < j < k \leq N, so we should print 0.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {

  public static void main(String[] args) {
    FastScanner fs = new FastScanner();
    int n = fs.nextInt();
    int[] arr = fs.readArray(n);
    int count = 0;
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        for (int k = j + 1; k < n; k++) {
          if ((arr[i] != arr[j] && arr[j] != arr[k] && arr[k] != arr[i]) && isValidTriangle(arr[i], arr[j], arr[k])) {
//            System.out.println(arr[i] + " " + arr[j] + " " + arr[k]);
            count++;
          }
        }
      }
    }
    System.out.println(count);
  }

  private static boolean isValidTriangle(int a, int b, int c) {
    return !(
        (a + b <= c) ||
        (a + c <= b) ||
        (b + c <= a)
    );
  }

  static class FastScanner {

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");

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

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

    int[] readArray(int n) {
      int[] a = new int[n];
      for (int i = 0; i < n; i++) {
        a[i] = nextInt();
      }
      return a;
    }

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