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.IO;
using System.Linq;
using System.Collections.Generic;
using static System.Math;
using static System.Console;
using static System.Linq.Enumerable;
using static System.Numerics.BitOperations;

namespace ABC175
{
    class SolverB
    {
        static void Main()
        {
            SetOut(new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false});
            new SolverB().Solve();
            Out.Flush();
        }

        public void Solve()
        {
            var N = Get.Int();
            int[] L = Get.Ints();
            Array.Sort(L);
            int len = L.Length;
            long ans = 0;
            for(int i=0; i<len; i++){
                for(int j=i+1; j<len; j++){
                    for(int k=j+1; k<len; k++){
                        if(L[i]+L[j] > L[k] && L[i] != L[j] && L[j] != L[k] && L[k] != L[i]){
                            ans++;
                            // WriteLine($"{L[i]}, {L[j]}, {L[k]}");
                        }
                    }
                }
            }
            WriteLine(ans);
        }




        static class Get
        {
            public static string Str() => ReadLine().Trim();
            public static int Int() => int.Parse(Str());
            public static long Long() => long.Parse(Str());
            public static double Double() => double.Parse(Str());
            public static string[] Strs() => Str().Split(' ', StringSplitOptions.RemoveEmptyEntries);
            public static int[] Ints() => Strs().Select(int.Parse).ToArray();
            public static long[] Longs() => Strs().Select(long.Parse).ToArray();
            public static double[] Doubles() => Strs().Select(double.Parse).ToArray();
            static bool TypeEq<T,U>() => typeof(T).Equals(typeof(U));
            static T TypeConv<T,U>(U u) => (T)Convert.ChangeType(u, typeof(T));
            static T TypeConv<T>(string s) => TypeEq<T, int>() ?   TypeConv<T, int>(int.Parse(s))
                                        : TypeEq<T, long>() ?       TypeConv<T, long>(long.Parse(s))
                                        : TypeEq<T, double>() ?     TypeConv<T, double>(long.Parse(s))
                                        : TypeConv<T, string>(s);
            public static (T,U) Tuple<T,U>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); return(t,u);}
            public static (T,U,V) Tuple<T,U,V>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); V v = TypeConv<V>(strs[2]); return(t,u,v);}
        }
    }
}