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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Collections;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Threading.Tasks;

class Program
{
	//Main
	static void Main(string[] args)
	{
		//出力準備（AutoFlushを切る）
		var sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
		Console.SetOut(sw);
		//解答
		Solve();
		//出力終了
		Console.Out.Flush();
	}

	static void Solve()
	{
		//読み込む
		int N = int.Parse(Console.ReadLine());
		long[] Ln = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();

		long ans = 0;

		//全探索
		for(int i=0; i<N-2; i++){
			for(int j=i+1; j<N-1; j++){
				if(Ln[i] == Ln[j]){
					continue;
				}
				for(int k=j+1; k<N; k++){
					if(Ln[i] == Ln[k] || Ln[j] == Ln[k]){
						continue;
					}
					
					//成立条件
					if(Ln[i] + Ln[j] > Ln[k] && Ln[j] + Ln[k] > Ln[i] && Ln[k] + Ln[i] > Ln[j]){
						ans ++;
					}
				}
			}
		}

		Console.WriteLine(ans);

	}
}