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.util.*;
 
public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int num = sc.nextInt();
    long array[] = new long[num];
    for(int i = 0;i < num;i++){
      array[i] = sc.nextLong();
    }
    long count = 0;
    for(int i = 0;i < num - 2;i++){
      for(int j = i + 1;j < num - 1;j++){
        for(int k = j + 1;k < num;k++){
          long a = array[i];
          long b = array[j];
          long c = array[k];
          long sum = a + b + c;
          if(a != b && b != c && c != a){
            long max = Math.max(a,Math.max(b,c));
            if(max < sum - max){
              count++;
            }
          }
        }
      }
    }
    System.out.println(count);
  }
}