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.Linq;
using System.Collections.Generic;
using System;

public class Hello
{
    public static void Main()
    {
        var d = new Dictionary<int, int>();
        var n = int.Parse(Console.ReadLine().Trim());
        string[] line = Console.ReadLine().Trim().Split(' ');
        for (int i = 0; i < n; i++)
        {
            var L = int.Parse(line[i]);
            if (d.ContainsKey(L)) d[L]++;
            else d[L] = 1;
        }
        getAns(d);
    }
    static void getAns(Dictionary<int, int> d)
    {
        var dc = d.Count();
        if (dc <= 2) { Console.WriteLine(0); return; }
        var a = new List<int>();
        foreach (var x in d) a.Add(x.Key);
        var count = 0;
        for (int i = 0; i < dc - 2; i++)
            for (int j = i + 1; j < dc - 1; j++)
                for (int k = j + 1; k < dc; k++)
                    if (check(a[i], a[j], a[k])) count += d[a[i]] * d[a[j]] * d[a[k]];
        Console.WriteLine(count);
    }
    static bool check(int a, int b, int c)
    {
        if (b + c <= a) return false;
        if (a + c <= b) return false;
        if (a + b <= c) return false;
        return true;
    }
}