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)

namespace ABC143.D
{
    using System;
    using System.Collections.Generic;
    using System.Linq;
    using static System.Console;



    public class Program
    {

        public static void Main(string[] args)
        {
            var n = ReadInputAsInt();
            var l = ReadInputsAsInt().ToList();
            WriteLine(Solve(l));

        }

        public static int Solve(List<int> l)
        {
            l.Sort();

            var sum = 0;
            //var minLen = l.Min();

            for (int a = l.Count - 1; a >= 2; a--)
            {
                if (l[a] >= l[a - 1] + l[a - 2]) continue;

                for (int b = a - 1; b >= 1; b--)
                {
                    if (l[a] >= l[b] + l[b - 1]) break;

                    for (int c = b - 1; c >= 0; c--)
                    {
                        if (l[b] + l[c] > l[a])
                        {
                            sum++;
                        }
                        else
                        {
                            break;
                        }
                    }
                }
            }

            return sum;
        }


        static IEnumerable<int> ReadInputsAsInt() => ReadLine().Split(' ').Select(x => int.Parse(x));

        static int ReadInputAsInt() => int.Parse(ReadLine());

    }
}