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;
class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());
        int[] l = InputIntArray();
        int count = 0;

        for (int a = 0; a < n; a++)
            for (int b = a + 1; b < n; b++)
                for (int c = b + 1; c < n; c++)
                {
                    int aa = l[a], bb = l[b], cc = l[c];
                    if (aa == bb || aa == cc || bb == cc)
                        continue;
                    if (aa + bb > cc && bb + cc > aa && cc + aa > bb)
                        count++;
                }
        Console.WriteLine(count);
    }


    public static int[] InputIntArray()
    {
        string[] strs = Console.ReadLine().Split(' ');
        int[] num = new int[strs.Length];
        for (int i = 0; i < num.Length; i++)
        {
            num[i] = int.Parse(strs[i]);
        }

        return num;

    }

}