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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static Scanner;

class Program
{
    static void Main() => new Program().Solve();

    public void Solve()
    {
        int n = ReadInt();
        int[] l = ReadInt(n).ToArray();
        int c = 0;
        for (int b = 0b111; b <= 1 << n; b = MyMath.NextCombination(b))
        {
            var x = new List<int>();

            for (int i = 0; i < n; i++)
            {
                if ((b & (1 << i)) != 0) x.Add(l[i]);
            }
            if (CanMake(x[0], x[1], x[2])) c++;
        }
        Console.WriteLine(c);
    }

    bool CanMake(int a, int b, int c)
    {
        return a != b && b != c && c != a && a + b > c && b + c > a && c + a > b;
    }
}

static class Scanner
{
    static Queue<string> que = new Queue<string>();
    public static string Read() { if (!que.Any()) foreach (var s in Console.ReadLine().Split()) que.Enqueue(s); return que.Dequeue(); }
    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static double ReadDouble() => double.Parse(Read());
    public static decimal ReadDecimal() => decimal.Parse(Read());
    public static IEnumerable<string> Read(long n) { for (long i = 0; i < n; i++) yield return Read(); }
    public static IEnumerable<int> ReadInt(long n) => Read(n).Select(int.Parse);
    public static IEnumerable<long> ReadLong(long n) => Read(n).Select(long.Parse);
    public static IEnumerable<double> ReadDouble(long n) => Read(n).Select(double.Parse);
    public static IEnumerable<decimal> ReadDecimal(long n) => Read(n).Select(decimal.Parse);
}

static class MyMath
{
    public static int NextCombination(int bit)
    {
        int x = bit & -bit;
        int y = x + bit;
        return y | (((bit & ~y) / x) >> 1);
    }
}