Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

namespace ConsoleApp5
{
    class Program
    {

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[] L = new int[N];
            String S = Console.ReadLine();
            String[] line = S.Split(' ');

            for(int i=0; i<N; i++)
            {
                L[i] = int.Parse(line[i]);
            }

            Array.Sort(L);

            int[,] wa = new int[N, N];

            for(int i=0; i<N-1; i++)
            {
                for(int j=i+1; j<N; j++)
                {
                    wa[i, j] = L[i] + L[j];
                }
            }

            int ans = 0;

            for(int k=N-1; k>=2; k--)
            {
                for (int i = 0; i < k; i++)
                {
                    for (int j = i + 1; j < k-1; j++)
                    {
                        if(wa[i,j] + L[k] / 2.0 > L[k])
                        {
                            ans++;
                        }

                    }
                }
            }

            Console.WriteLine(ans);

        }
    }
}