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.Collections.Generic;
using System.Linq;

public class ABC {
    private static void Main(string[] args) {
        var n = ReadInt();
        if (n < 3) { Console.WriteLine("0"); return; }
        var l = ReadIntsAsArrayAsc();
        Console.WriteLine(CountSuitableTriangle(0, 1, 2, 0, n, l));
    }

    private static int CountSuitableTriangle(int i, int j, int k, int count, int n, int[] l) {
        if ((l[i] + l[j] > l[k]) && (l[i] != l[j]) && (l[j] != l[k]) && (l[i] != l[k])) count++;
        if (k != n - 1) return CountSuitableTriangle(i, j, k + 1, count, n, l);
        else if (j != n - 2) return CountSuitableTriangle(i, j + 1, j + 2, count, n, l);
        else if (i != n - 3) return CountSuitableTriangle(i + 1, i + 2, i + 3, count, n, l);
        else return count;
    }

    private static int ReadInt() => int.Parse(Console.ReadLine().Trim());
    private static int[] ReadIntsAsArrayAsc() => Console.ReadLine().Trim().Split().Select(x => int.Parse(x)).OrderBy(x => x).ToArray();
}