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.IO.Pipes;
using System.Linq;
using System.Numerics;
using System.Text.RegularExpressions;
using System.Threading;

namespace Atcoder
{
	class Program
	{
		//string s = Console.ReadLine();
		//int[] intArray = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
		//int H = intArray[0];
		//int W = intArray[1];
		//int N = int.Parse(Console.ReadLine());
		//List<int> A = new List<int>(Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray());
		//Boolean ok = false;
		//List<int> dp = Enumerable.Repeat(個数, 値).ToList();

		//Console.WriteLine(ans);
		//Console.WriteLine("Yes");
		//Console.WriteLine("No");
		//Console.ReadKey();
		//Console.WriteLine(cnt);

		//string[] strArray = Console.ReadLine().Split(' ').ToArray();
		//string S = strArray[0];
		//string T = strArray[1];
		static void Main(string[] args)
		{
			int N = int.Parse(Console.ReadLine());
			int[] L = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
			int cnt = 0;
			if(N < 3)
            {
				Console.WriteLine(0);
				return;
			}

			for (int i = 0; i < N - 2; i++)
			{
				for (int j = i + 1; j < N - 1; j++)
				{
					if(L[i] == L[j])
						continue;
					for (int k = j + 1; k < N; k++)
					{
						if (L[i] == L[k] || L[j] == L[k])
							continue;
						int max = Math.Max(Math.Max(L[i], L[j]), L[k]);
						int sum = L[i] + L[j] + L[k];
						if (max * 2 >= sum)
							continue;
						cnt++;
					}

				}
			}
			Console.WriteLine(cnt);
		}

		/// <summary>
		/// 回文
		/// </summary>
		/// <param name="Target"></param>
		/// <param name="len"></param>
		/// <returns></returns>
		static bool Palindrome(string Target , int len)
        {
			bool yes = true;

			for(int i = 0;i < len; i++)
            {
				if(Target[i] != Target[len - 1 - i])
                {
					yes = false;
					break;
                }
            }
			return yes;
        }

		/// <summary>
		/// アナグラム
		/// </summary>
		/// <param name="word1"></param>
		/// <param name="word2"></param>
		/// <returns></returns>
		static bool IsAnagramOf(string word1, string word2)
		{
			return word1.OrderBy(x => x).SequenceEqual(word2.OrderBy(x => x));
		}
		/// <summary>
		/// 最小公倍数
		/// </summary>
		/// <param name="a"></param>
		/// <param name="b"></param>
		/// <returns></returns>
		public static BigInteger Lcm(BigInteger a, BigInteger b)
		{
			return a * b / Gcd(a, b);
		}

		/// <summary>
		/// 最大公約数
		/// </summary>
		/// <param name="a"></param>
		/// <param name="b"></param>
		/// <returns></returns>
		public static BigInteger Gcd(BigInteger a, BigInteger b)
		{
			if (a < b)
				// 引数を入替えて自分を呼び出す
				return Gcd(b, a);
			while (b != 0)
			{
				var remainder = a % b;
				a = b;
				b = remainder;
			}
			return a;
		}
	}
}