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;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp4
{
	class Program
	{
		static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			var l = (from lx in Console.ReadLine().Split()
					 let x = int.Parse(lx)
					 orderby x descending
					 select x).ToArray<int>();

			int count = 0;
			int prea = 0, preb = 0, prec = 0;
			for (int i = 0; i < n - 2; i++)
			{
				int a = l[i];
				for (int j = i + 1; j < n - 1; j++)
				{
					int b = l[j];
					if (a >= b * 2)
					{
						break;
					}
					if (a == prea && b == preb)
					{
						continue;
					}
					for (int k = j + 1; k < n; k++)
					{
						int c = l[k];
						if (a >= b + c)
						{
							break;
						}
						if (a == prea && b == preb && c == prec)
						{
							continue;
						}
						else
						{
							count++;
							prea = a;
							preb = b;
							prec = c;
						}
					}
				}
			}
			Console.WriteLine(count);
		}
	}
}