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 Program {
    static void Main(string[] args) {

        int N = int.Parse(Console.ReadLine());
        string[] L = Console.ReadLine().Split(' ');

        Array.Sort(L);

        int result = 0;

        for (int a = L.Length-1; a >= 2; a--) {
            int c = 0;
            for(int b = a - 1; b > c;b--) {
                int la = int.Parse(L[a]);
                int lb = int.Parse(L[b]);
                int lc = int.Parse(L[c]);

                while (lb + lc <= la && b > c) {
                    c++;
                    lc = int.Parse(L[c]);
                }
                result += b - c;
            }
        }

        Console.WriteLine(result);

    }
}