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;

namespace _175_b
{
    internal class MakingTriangle
    {
        private static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine() ?? throw new InvalidOperationException());
            var l = Console.ReadLine()?.Split(" ").Select(int.Parse).ToArray();

            if (n < 3)
            {
                Console.WriteLine(0);
                return;
            }
            if (l == null) return;

            var count = 0;
            for (var i = 0; i < n; i++)
            {
                for (var j = i + 1; j < n; j++)
                {
                    for (var k = j + 1; k < n; k++)
                    {
                        if (IsDifferentLength(l[i], l[j], l[k]))
                        {
                            if(IsTriangle(l[i], l[j], l[k]))
                            {
                                count++;
                            }
                        }
                    }
                }
            }

            Console.WriteLine(count);
        }

        private static bool IsTriangle(int a, int b, int c)
        {
            return a + b > c && b + c > a && c + a > b;
        }

        private static bool IsDifferentLength(int a, int b, int c)
        {
            return a != b && b != c && c != a;
        }
    }
}