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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;

public class Program{
    public static void Main(){
        int times = int.Parse(Console.ReadLine());
        int[] sticks = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        int result = 0;
        
        for (int i = 0; i < sticks.Count() - 2; i++){
            for (int j = i + 1; j < sticks.Count() - 1; j++){
                for (int k = j + 1; k < sticks.Count(); k++){
                    int[] targetSticks = new int[] {sticks[i], sticks[j], sticks[k]};
                    Array.Sort(targetSticks);
                    if (targetSticks[0] != targetSticks[1] && targetSticks[1] != targetSticks[2]){
                        if (targetSticks[0] + targetSticks[1] > targetSticks[2]) result++;
                    }
                }
            }
        }
        
        Console.WriteLine(result);
    }
}