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 inputInt = int.Parse(Console.ReadLine());
            var inputArr = Console.ReadLine().Split().Select(int.Parse).ToArray();

            int ans = 0;
            //string ans = "";

            //降順に並べ替え
            inputArr = inputArr.OrderByDescending(x => x).ToArray();

            //長いものから順に選んでいく
            int N = inputInt;
            for(int i = 0; i < N - 2; i++)
            {
                for(int j = i + 1; j < N - 1; j++)
                {
                    //O(N^2)
                    ans += CountC(inputArr, j, inputArr[i] - inputArr[j]);
                }
            }

            Console.WriteLine(ans);
            Console.ReadKey();
        }

        static int CountC(int[] Arr, int pos, int largerThan)
        {
            int ans = 0;
            ans = Arr.Skip(pos + 1).Where(x => x > largerThan).Count();

            return ans;
        }
    }
}