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;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder_solve
{
    class Program
    {
        public const ulong mod = 1000000007;

        static void Main(string[] args)

        {
            var n = Input();
            var s = Input3();
            long ans = 0;

            Array.Sort(s);

            for(long i = 0; i < n-2; i++)
            {
                for(long j=i+1;j<n-1;j++)
                
                    for(long k = j + 1; k < n ; k++)
                    {
                        if ( s[k] < s[i] + s[j] && s[i] < s[k] + s[j] && s[j] < s[i] + s[k]) ans++;
                       if (s[i] + s[j] < s[k]) break;


                    }
                
            }

            Console.WriteLine(ans);


        }

       
        static public long Input()
        {
            return long.Parse(Console.ReadLine());
        }

        static public string[] Input2()
        {
            return Console.ReadLine().Split();
        }

        static public long[] Input3()
        {
            string[] data = Console.ReadLine().Split();
            long[] res = new long[data.LongLength];
            for(long i = 0; i < data.LongLength; i++)
            {
                res[i] = long.Parse(data[i]);
            }
            return res;
        }
        public static long Choose(long n, long a)
        {
            long x = 1;
            long y = 1;
            for (long i = 0; i < a; i++)
            {
                x *= n - i;
                y *= i + 1;
            }
            return x / y;
        }
    }
}