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: Time Limit Exceeded)

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

namespace ConsoleApp2
{


    public class Program
    {

        static long D = (long)Math.Pow(10, 9) + 7;

        public static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            int[] Ls = Read(Console.ReadLine());

            Array.Sort(Ls);

            int count = 0;
            for (int i = 0; i < Ls.Length-2; i++)
            {
                for (int j = i+1; j < Ls.Length-1; j++)
                {
                    for (int k = j+1; k < Ls.Length; k++)
                    {
                        if (Ls[i] + Ls[j] > Ls[k]) count++;
                        else break;
                    }
                }
            }

            Console.WriteLine(count);
            Console.ReadLine();

        }

        private static int[] Read(string input)
        {
            string[] strings = input.Split(' ');
            int num = strings.Length;
            int[] ints = new int[num];
            for (int i = 0; i < num; i++)
            {
                ints[i] = int.Parse(strings[i]);
            }
            
            return ints;
        }


    }


}