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: Runtime Error)

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

namespace ConsoleApp3
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var lengths = Console.ReadLine().Split(" ").Select(x => decimal.Parse(x)).ToArray();

            var combinations = GetCombinations(n, lengths).ToArray();

            var allTriangleCount = combinations.Count(x =>
            {
                var maxLine = x.Max();
                var otherSum = x.Except(new decimal[] { maxLine }).Sum();

                return maxLine < otherSum;
            });

            Console.WriteLine(allTriangleCount);
        }

        private static IEnumerable<decimal[]> GetCombinations(int n, decimal[] lengths)
        {
            var combination = new Combination(n, 3);

            while (combination != null)
            {
                yield return combination.data.Select(x => lengths[x]).ToArray();
                combination = combination.Successor();
            }
        }

        private class Combination
        {
            private long n = 0;
            private long k = 0;
            public long[] data = null;

            public Combination(long n, long k)
            {
                if (n < 0 || k < 0)
                {
                    throw new Exception("Negative parameter in constructor");
                }

                this.n = n;
                this.k = k;
                this.data = new long[k];

                for (long i = 0; i < k; ++i)
                {
                    this.data[i] = i;
                }
            }

            public Combination Successor()
            {
                if (this.data.Length == 0 ||
                    this.data[0] == this.n - this.k)
                {
                    return null;
                }

                Combination answer = new Combination(this.n, this.k);

                long i;
                for (i = 0; i < this.k; ++i)
                {
                    answer.data[i] = this.data[i];
                }

                for (i = this.k - 1; i > 0 && answer.data[i] == this.n - this.k + i; --i) ;

                ++answer.data[i];

                for (long j = i; j < this.k - 1; ++j)
                {
                    answer.data[j + 1] = answer.data[j] + 1;
                }

                return answer;
            }

            public string[] ApplyTo(string[] strarr)
            {
                if (strarr.Length != this.n)
                {
                    throw new Exception("Bad array size");
                }

                string[] result = new string[this.k];

                for (long i = 0; i < result.Length; ++i)
                {
                    result[i] = strarr[this.data[i]];
                }

                return result;
            }

            public static long Choose(long n, long k)
            {
                if (n < 0 || k < 0)
                {
                    throw new Exception("Invalid negative parameter in Choose()");
                }

                if (n < k)
                {
                    return 0;
                }

                if (n == k)
                {
                    return 1;
                }

                long delta, iMax;

                if (k < n - k)
                {
                    delta = n - k;
                    iMax = k;
                }
                else
                {
                    delta = k;
                    iMax = n - k;
                }

                long answer = delta + 1;

                for (long i = 2; i <= iMax; ++i)
                {
                    checked { answer = (answer * (delta + i)) / i; }
                }

                return answer;
            }

            public override string ToString()
            {
                StringBuilder sb = new StringBuilder();

                sb.Append("{ ");

                for (long i = 0; i < this.k; ++i)
                {
                    sb.AppendFormat("{0} ", this.data[i]);
                }

                sb.Append("}");

                return sb.ToString();
            }
        }
    }
}