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 static System.Console;

namespace abc175
{
    class Program
    {
        static long[] ReadNumList()
        {
            var line = Console.ReadLine().Split(' ');
            if (line.Length == 1 && string.IsNullOrEmpty(line[0]))
            {
                return new long[0];
            }
            var numList = new long[line.Length];
            for (var i = 0; i < line.Length; ++i)
            {
                numList[i] = long.Parse(line[i]);
            }
            return numList;
        }
        static void Main()
        {
            var n = int.Parse(ReadLine());
            var lList = ReadNumList();
            var count = 0;
            for (var i = 0; i < n - 2; ++i)
            {
                for (var j = i + 1; j < n - 1; ++j)
                {
                    if (lList[i] == lList[j])
                    {
                        continue;
                    }
                    for (var k = j + 1; k < n; ++k)
                    {
                        if (lList[i] == lList[k] || lList[j] == lList[k])
                        {
                            continue;
                        }
                        if ((lList[i] + lList[j]) > lList[k] &&
                            (lList[j] + lList[k]) > lList[i] &&
                            (lList[k] + lList[i]) > lList[j])
                        {
                            ++count;
                        }
                    }
                }
            }
            WriteLine(count);
        }
    }
}