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.Diagnostics;
using System.IO;
using System.Linq;

namespace MyProject
{
    class Program
    {
        static void Main(string[] args)
        {
#if Local
            var sw = new Stopwatch();
            sw.Start();
            Console.SetIn(new StreamReader("input.in"));
#endif

            var solver = new Solver();
            solver.Solve();
#if Local
            Console.WriteLine($"{sw.ElapsedMilliseconds}ms");
#endif
        }
    }

    class Solver
    {
        public void Solve()
        {
            var N = int.Parse(Console.ReadLine());
            var L = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

            var answer = 0;
            for (int i = 0; i < L.Length; i++)
            {
                var a = L[i];
                for (int j = i + 1; j < L.Length; j++)
                {
                    var b = L[j];
                    if (!(a - b < a + b) || !(b - a < a + b))
                    {
                        continue;
                    }

                    for (int k = j + 1; k < L.Length; k++)
                    {
                        var c = L[k];
                        if (a < b + c && b < c + a && c < a + b)
                        {
                            answer++;
                        }
                    }
                }
            }

            Console.WriteLine(answer);
        }
    }
}