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

namespace AtCoderWorkspace
{
    public class Solver
    {
        public void Solve()
        {
            var cin = new Scanner();
            var n = cin.nextInt();
            var aa = cin.ArrayLong(n);

            var ans = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = i+1; j < n; j++)
                {
                    for (int k = j+1; k < n; k++)
                    {
                        var a = aa[i];
                        var b = aa[j];
                        var c = aa[k];

                        if (a == b || b == c || c == a) continue;

                        if (a < b + c && b < a + c && c < a + b)
                        {
                            ans++;
                        }
                    }
                }
            }

            Console.WriteLine(ans);
            
        }
    }

    public static class Combination
    {
        public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
        {
            if (k == 1)
            {
                foreach (var item in items)
                    yield return new T[] { item };
                yield break;
            }
            foreach (var item in items)
            {
                var leftside = new T[] { item };

                var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }
        }
    }

    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public int[] DPArrayInt(int N, int ex)
        {
            int[] Array = new int[N + ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt();
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public long[] DPArrayLong(int N, int ex)
        {
            long[] Array = new long[N + ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong();
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }

    class Program
    {
        static void Main(string[] s) => new Solver().Solve();
    }
}