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;
using System.IO;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    class AtCoderr
    {
        static void Main(string[] args)
        {
            int n = int.Parse(ReadLine());
            int[] s = ReadLine().Split(' ').Select(int.Parse).ToArray();
            long ans = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = i+1; j < n; j++)
                {
                    for (int k = j+1; k < n; k++)
                    {
                        if (s[i] < s[j] + s[k])
                        {
                            if (s[j] < s[i] + s[k])
                            {
                                if (s[k] < s[j] + s[i])
                                {
                                    ans++;
                                }
                            }
                        }
                    }
                }
            }
            WriteLine(ans);
        }
    }
}