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: Wrong Answer)

using System;
class P
{
    static void Main()
    {
        string a = Console.ReadLine();
        int[] L = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

        int i_j;
        int j_i;
        Array.Sort(L);
        int count = 0;
        int LL = L.Length;

        for (int i = 0; i < LL - 2; i++)
        {
            for (int j = i + 1; L[j] > L[LL - 1] - L[i]; j++)
            {
                j_i = L[j] - L[i];
                i_j = L[i] - L[j];

                for (int k = j + 1; L[i] + L[j] > L[k]; k++)
                {
                    if (i_j >= 0 && L[k] > i_j) { count++; }
                    else if (i_j == 0) { if (L[i] != L[k]) { count++; } }
                    else if (L[k] > j_i) { count++; }

                    if (k + 1 == LL) { break; }
                }
                if (j + 2 == LL) { break; }
            }
        }

        
        Console.WriteLine(count);
    }
}