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.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Security.Cryptography.X509Certificates;
using System.Diagnostics;
using System.Reflection.Metadata;
using System.Threading;

namespace AtCoder
{
    class Program
    {

        struct Point
        {
            public int left;
            public int right;

            public Point(int left, int right)
            {

                this.left = left;
                this.right = right;

            }

        }


        const int BiggestMod = 1000000007;

        public static void Main()
        {

            long ans = 0;
            var num = int.Parse(Console.ReadLine());

            if (num < 3)
            {

                Console.WriteLine(0);
                return;

            }

            var buf = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();

            Array.Sort(buf);
            Array.Reverse(buf);

            for (int i = 0; i + 2 < num; i++)
                for (int j = i + 1; j + 1 < num; j++)
                    if (buf[i] != buf[j])
                        for (int k = j + 1; k < num; k++)
                            if (buf[j] != buf[k])
                                if (buf[i] < buf[j] + buf[k])
                                    ans++;

            Console.WriteLine(ans);

        }

    }

}