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.Collections;
using System.Linq;


class Program
{
    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var l = Console.ReadLine().Split(' ').Select(int.Parse).OrderBy(v => v).ToArray();

        var ret = 0;
        for (var a = 0; a < n - 2; ++a)
        {
            var b = a + 1;
            while (b < n - 1 && l[b] < (l[a] + (l[a] + l[b] - 1)) && l[a] < (l[b] + (l[a] + l[b] - 1)))
            {
                ret += l.Skip(b + 1).Where(c => c < (l[a] + l[b])).ToArray().Length;
                ++b;
            }
        }

        Console.Write(ret);
    }
}