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;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = short.Parse(Console.ReadLine());
            var array = Console.ReadLine().Split().Select(short.Parse).OrderBy(_ => _).ToArray();

            //var ggg = array.GroupBy(n => n)
            //    .OrderBy(n => n)
            //    .Select(g => new { g.Key, Count = g.Count() });


            //var str = string.Join(" ", Enumerable.Range(1, 2000));
            //var N = 2000;
            //var array = str.Split().Select(short.Parse).OrderBy(_ => _).ToArray();

            //var aaa = new SortedList<short, short>();
            //foreach (var item in array)
            //{
            //    aaa.Add(item, item);
            //}

            var count = 0;

            for (int i = 0; i < N - 2; i++)
            {
                var a = array[i];

                for (int j = i + 1; j < N - 1; j++)
                {
                    var b = array[j];
                    //if (a >= b) continue;

                    var ab = a + b;
                    for (int k = j + 1; k < N; k++)
                    {
                        var c = array[k];

                        if (c >= ab) break;
                        if (b >= c + a) continue;
                        if (a >= b + c) continue;

                        count++;
                    }
                }
            }

            Console.WriteLine(count);
        }
    }
}