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.Collections.Generic;
using System.Linq;

namespace Q4
{
    class MainClass
    {
        public static void Main(string[] args)
        {
            int N = Int32.Parse(Console.ReadLine());
            string [] input = Console.ReadLine().Split(' ');
            var list = new List<int>();
            for(int i = 0; i < N; i++)
            {
                list.Add(Int32.Parse(input[i]));
            }
            list.Sort();

            int count = 0;
            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 (list[k] < list[i] + list[j])
                        {
                            count++;
#if DEBUG
                            Console.WriteLine($"DEBUG: {i}, {j}, {k}");
                            Console.WriteLine($"{list[i]}, {list[j]}, {list[k]}");
#endif
                        }
                        else
                            break;
                    }
                }
            }

            Console.WriteLine(count);
        }
    }
}