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;

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            string[] sl = Console.ReadLine().Split(' ');
            int[] Li = new int[N]; 
            for (int i = 0; i<N; i++)
            {
                Li[i] = int.Parse(sl[i]);
            }

            Array.Sort(Li);
            //Array.Reverse(Li);

            int ans = 0;

            for (int i = N-1; i >= 2; i--)
            {
                for (int j = i - 1 ; j >= 1; j--)
                {
                    for (int k = j - 1; k >= 0; k--)
                    {
                        if (Li[i] < (Li[j] + Li[k]))
                        {
                            //Console.WriteLine("i-j-k"+i.ToString()+"-"+j.ToString()+"-"+k.ToString()+" "+Li[i].ToString() + "," + Li[j].ToString() + "," + Li[k].ToString());
                            ans++;
                        }
                        else
                        {
                            break;
                        }
                    }
                }
            }

            //for(int i = 0; i<N-2; i++)
            //{
            //    for(int j = i + 1; j<N-1; j++)
            //    {
            //        for(int k = j+1; k<N; k++)
            //        {
            //            if (Li[i] < (Li[j] + Li[k]))
            //            {
            //                //Console.WriteLine("i-j-k"+i.ToString()+"-"+j.ToString()+"-"+k.ToString()+" "+Li[i].ToString() + "," + Li[j].ToString() + "," + Li[k].ToString());
            //                ans++;
            //            }
            //            else
            //            {
            //                break;
            //            }
            //        }
            //    }
            //}
            Console.WriteLine(ans);
            //Console.ReadKey();

        }
    }
}