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;
namespace ABC143D
{
    public class EmptyClass
    {
        public static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] l = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            int cnt = 0;
            for (int i = 0; i < n - 2; i++)
            {
                for (int j = i + 1; j < n - 1; j++)
                {
                    int a = l[i];
                    int b = l[j];
                    var x = l.Skip(j+1).Where(c => a < b + c && b < a + c && c < a + b).Count();
                    cnt += x;
                }
            }
            Console.WriteLine(cnt);
        }
    }
}