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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;

namespace D
{
    class Program
    {
        static int B(int[] ABC,int N)
        {
            Array.Sort(ABC);
            int sum = 0;

            for (int a=0; a<N-2; a++)
            {
                for (int b = a + 1; b < N - 1; b++)
                {
                    for (int c = N - 1; c > 0; c--)
                    {
                        int d = ABC[c] - ABC[a] - ABC[b];
                        if (d < 0)
                        {
                            sum += c - b;
                            break;
                        }
                    }
                }
            }
            return sum;
        }
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string[] L = Console.ReadLine().Split(' ');
            int[] ABC = new int[N];

            for(int i=0;i<N;i++)
            {
                ABC[i] = int.Parse(L[i]);
            }

            //int result = A(ABC, N);
            int result = B(ABC, N);
            Console.WriteLine(result);
        }
    }
}