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 AtCoder.Abc
{
    class QuestionB
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var n = int.Parse(Console.ReadLine());
            var l = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();

            int cnt = 0;
            for (int i = 0; i < (n-2); i++)
            {
                for (int j = i+1; j < (n-1); j++)
                {
                    for (int k = j+1; k < n; k++)
                    {
                        if (CanTriangle(l[i], l[j], l[k]))
                        {
                            cnt++;
                        }
                    }
                }
            }
            Console.WriteLine(cnt);

            Console.Out.Flush();
        }
        public static bool CanTriangle(int i, int j, int k)
        {
            if (i == j || i == k || j == k) return false;
            var a = new int[] { i, j, k };
            var b = a.OrderBy(i => i).ToArray();
            return (b[0] + b[1]) > b[2];
        }
    }
}