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.Numerics;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using System.Collections;

namespace debug
{
    class main
    {
        static void Main(string[] args)
        {
            //問題クラスを展開
            ProgramB a = new ProgramB();
            a.main();//実行する

        }

    }
    //ABC175
    class ProgramA
    {
        public void main()
        {
            //入力
            string s = Console.ReadLine();

            //30以上ならYes、それ以外はNoを出力
            if (s == "RRR")
                Console.WriteLine(3);
            else if(s == "RRS" || s == "SRR")
                Console.WriteLine(2);
            else if (s == "SSS")
                Console.WriteLine(0);
            else
                Console.WriteLine(1);

        }
    }

    class ProgramB
    {
        public void main()
        {
            //入力

            int n = int.Parse(Console.ReadLine());
            string[] s = Console.ReadLine().Split(' ');

            long count = 0;
            //それぞれの距離を求めて、距離がD以下なら1足す
            for (int i = 0; i < n; i++)
                for (int j = i + 1; j < n; j++)
                    for (int k = j + 1; k < n; k++)
                    {
                        long a = long.Parse(s[i]);
                        long b = long.Parse(s[j]);
                        long c = long.Parse(s[k]);
                        if (a == b || b == c || c == a)
                            continue;

                        if (a + b> c  && b + c > a && c +a > b)
                            count++;
                    }

            //答え出力
            Console.WriteLine(count);

        }
    }

    class ProgramC
    {
        public void main()
        {

            //入力
            int k = int.Parse(Console.ReadLine());

            //偶数なら答えは-1
            if(k % 2 == 0)
            {
                Console.WriteLine("-1");
                return;
            }

            //k = 1から7なら答えは1
            if (7 % k == 0)
            {
                Console.WriteLine("1");
                return;
            }


            int flag = 0;
            long num = 7;
            long count = 1;

            //項は10倍して7足すなので、modで管理。modKで0なら答え出力。
            while(flag == 0)
            {
                count++;//項を進める
                num *= 10;
                num += 7;
                num %= k;//10倍して7足したものをmodKで管理
                if (num == 0)
                    flag = 1;
                //もし10の7乗以上の項なら答えはないので-1で終わり
                if (count >= 10000000)
                {
                    Console.WriteLine("-1");
                    return;
                }
                
            }

            //答え出力
            Console.WriteLine(count);




        }
    }

    class ProgramD
    {
        public void main()
        {

            //入力
            long n = long.Parse(Console.ReadLine());
            string s = Console.ReadLine();

            int wc = 0;
            int rc = 0;
            //まずは赤と白の石の数を数える
            for (int i = 0; i < n; i++)
            {
                if (s[i] == 'R')
                    rc++;
                else
                    wc++;
            }

            //白が0なら0（冷静に赤が0なら0だがこの下に通しても通る）
            if (wc == 0)
            {
                Console.WriteLine("0");
                return;
            }

            int rw = 0;
            int ww = 0;

            //左から赤の数だけ並べる。不一致の白の数を数える
            for (int i = 0; i < rc; i++)
            {
                if (s[i] == 'W')
                    rw++;
            }

            //残りは白。不一致の赤の数を数える
            for (int i = rc; i < n; i++)
            {
                if (s[i] == 'R')
                    ww++;
            }

            
            //答は、赤か白の違う数の小さい方と絶対値の差の和を足す
            Console.WriteLine(Math.Min(rw,ww) + Math.Abs(rw - ww));
            

        }

    }

    class ProgramE
    {

        public void main()
        {
            //入力
            string[] s = Console.ReadLine().Split(' ');
            long n = long.Parse(s[0]);
            long k = long.Parse(s[1]);

            long[] a = new long[n];

            string[] t = Console.ReadLine().Split(' ');

            for(int i = 0;i < n;i++)
                a[i] = long.Parse(t[i]);

            long min = 0;//最初を0にすると1に答えができる
            long max = 1000000000;//答候補の最大

            //二分探索（答えを決め打ちして、切る回数を数える。k回以下ならmax,そうでないならmin)
            //小さくした方が回数がかかるので、maxが満たす最小の丸太の長さ
            while(min + 1 != max)
            {
                long temp = (min + max) / 2;
                long cut = 0;
                //切る回数を数える
                for (int i = 0; i < n; i++)
                {
                    //tempが大きいなら切らない
                    if (a[i] < temp)
                        continue;
                    //割り切れるかどうかで回数は変わる
                    if(a[i] % temp == 0)
                        cut += a[i] / temp - 1;
                    else
                        cut += a[i] / temp;
                }

                //k回以下ならmax更新、そうでないならminを更新
                if (cut <= k)
                    max = temp;
                else
                    min = temp;

            }

            //答え出力
            Console.WriteLine(max);

        }


    }

}