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;

class Atcoder
{
    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());

        var s = Console.ReadLine().Split().Select(int.Parse).ToArray();

        long count = 0;

        for (int i = 0; i < s.Length; i++)
        {
            for (int j = 0; j < s.Length; j++)
            {
                if (i == j)
                {
                    continue;
                }
                for (int k = 0; k < s.Length; k++)
                {
                    if (i == k || j == k)
                    {
                        continue;
                    }
                    if (s[i] < s[j] + s[k] &&
                        s[j] < s[i] + s[k] &&
                        s[k] < s[i] + s[j])
                    {
                        count++;
                    }
                }
            }
        }


        Console.WriteLine(count/6);

    }
}