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: Wrong Answer)

using System;
class Program {
    static void Main (string[] args) {
        int i, j, k, n = 0;
        int N = int.Parse (Console.ReadLine ());
        string[] input = Console.ReadLine ().Split (' ');
        int[] L = new int[N];
        for (i = 0; i < N; i++)
            L[i] = int.Parse (input[i]);
        for (i = 0; i < N; i++)
            for (j = 0; j < N; j++)
                for (k = 0; k < N; k++)
                    if (i < j && j < k)
                        if (L[i] > 0 && L[j] > 0 && L[k] > 0)
                            if (i != j && j != k && k != i)
                                if (L[i] != L[j] && L[j] != L[k] && L[k] != L[i])
                                    if (i + j > k && j + k > i && k + i > j)
                                        n += (L[i] * L[j] * L[k]);
        Console.WriteLine (n);
    }
}