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;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
using System.Threading;
using System.IO.Pipes;
using System.ComponentModel;
using System.Drawing;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            String S = Console.ReadLine();

            long[] Arr = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

            int ans = 0;

            long max;
            long sum;

            for (int i = 0; i < Arr.Length; i++) 
            {
                for (int j = i; j < Arr.Length; j++)
                {
                    for (int k = i+1; k < Arr.Length; k++)
                    {
                        if (Arr[i] != Arr[j] && Arr[i] != Arr[k] && Arr[j] != Arr[k])
                        {
                            max = Math.Max(Arr[i], Math.Max(Arr[j],Arr[k]));
                            sum = Arr[i] + Arr[j] + Arr[k];
                            if (sum - max > max) 
                            {
                                ans++;
                            }
                        }

                    }

                }

            }
            ans = ans / 2;

            Console.WriteLine(ans);

        }

    }
}