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;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
class Program{
  static void Main()
  {
    int number = int.Parse(Console.ReadLine());
    if(number < 3) {
      Console.WriteLine(0);
    }
    else{
       string[] numbersString = Console.ReadLine().Split(' ');
       List<int> numbers = new List<int>();
       for (int i = 0; i < number; i++)
       {
         numbers.Add(int.Parse(numbersString[i]));
       }
    
       var convinations = GetCombination(numbers, 3);
       int result = 0;
       foreach(var combi in convinations)
       {
         int a = combi[0];
         int b = combi[1];
         int c = combi[2];
         bool zeroExists = a==0 || b==0 || c==0;
         bool diff = !(a==b || b==c || a==c);
         bool canBeTriangle = a+b>c || a+c>b || b+c>a;
         if(diff && canBeTriangle) result++;
       }
       Console.WriteLine(result);
    }
  }
  
  static List<List<int>> GetCombination(List<int> self, int n)
    {
        return Enumerable.Range(0, n-1)
          .Aggregate(
                Enumerable.Range( 0, self.Count - n + 1 )
                    .Select( num => new List<int> { num } ),
                ( list, _ ) => list.SelectMany(
                    c => Enumerable.Range( c.Max() + 1, self.Count - c.Max() - 1 )
                            .Select( num => new List<int>( c ) { num } )))
            .Select(c => c.Select( num => self[ num ] )
                    .ToList())
          .ToList();
    }
}