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.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var N = int.Parse(Console.ReadLine());
        var L = new List<long>();
        var input = Console.ReadLine().Split(" ");

        for (int i = 0; i < N; i++)
        {
            L.Add(long.Parse(input[i]));
        }

        var count = 0;
        for(int i = 0; i < N; i++)
        {
            for(int j = i + 1; j < N; j++)
            {
                for(int k = j + 1; k < N; k++)
                {
                    var side = new List<long>();
                    side.Add(L[i]);
                    side.Add(L[j]);
                    side.Add(L[k]);
                    side.Sort();

                    if (side.Distinct().Count() != 3) continue;
                    if ((side[0] + side[1]) > side[2]
                        && (side[1] + side[2]) > side[0]
                        && (side[2] + side[0]) > side[1]) count++;
                }
            }
        }

        Console.WriteLine(count);

    }
}