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;

namespace ABC143D
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var Ls = Console.ReadLine().Split().Select(x => int.Parse(x));
            var ans = 0;

            foreach (var lines in Combination(Ls, 3).Where(x => x[0] < x[1] + x[2] && x[1] < x[2] + x[0] && x[2] < x[0] + x[1]))
                ans++;
          
            Console.WriteLine(ans);
        }

        static IEnumerable<T[]> Combination<T>(IEnumerable<T> items, int k)
        {
            if (k == 1)
            {
                foreach (var item in items)
                    yield return new T[] { item };
                yield break;
            }
            foreach (var item in items)
            {
                var leftside = new T[] { item };

                var unused = items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                foreach (var rightside in Combination(unused, k - 1))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }
        }
    }
}