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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var L = Console.ReadLine().Split().Select(int.Parse).ToArray();

            var triangles = new HashSet<string>();
            for (var a = 0; a < N; a++)
            {
                for (var b = a; b < N; b++)
                {
                    if (a == b) continue;
                    for (var c = b; c < N; c++)
                    {
                        if (a == c || b == c) continue;
                        if (L[a] < L[b] + L[c] && L[b] < L[c] + L[a] && L[c] < L[a] + L[b])
                        {
                            var array = new int[] { a, b, c };
                            Array.Sort(array);
                            triangles.Add(string.Join("", array));
                        }
                    }
                }
            }

            Console.WriteLine(triangles.Count);
        }
    }
}