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: Accepted)

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

namespace FreeWorks
{
    class Program
    {
        static int Bs(int[] array, int left, int right, int target)
        {
            
            int save_left = left;
            if (array[left] >= target) return 0;
            else if (array[right] < target) return right - left + 1;
            else if (left + 1 == right) return 1;

            while (left < right - 1)
            {
                int m = (left + right) / 2;
                if (array[m] < target) left = m;
                else right = m;
            }
            if (array[right] < target) return right - save_left + 1;
            else return right - save_left;
                    
        }

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[] L = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).OrderBy(x => x).ToArray();
            int cnt = 0;
            
            for (int a = 0; a < N - 2; a++)
            {
                for (int b = a + 1; b < N - 1; b++)
                {
                    int t = L[a] + L[b];
                    int l = b + 1;
                    int r = N - 1;
                    int test = Bs(L, l, r, t);
                    cnt += test;          
                }
            }

                    Console.WriteLine(cnt);
        }   
    }
}