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;
class Program
{
	static void Main(string[] args)
	{
		// 個数の入力
		int n = int.Parse(Console.ReadLine());
		// 長さ入力
		string[] input = Console.ReadLine().Split(' ');
		int[] lens = new int[input.Length];
		int count = 0;
		for (int i = 0; i < n; i++) lens[i] = int.Parse(input[i]);
		for (int i = 0; i < n; i++) for (int j = i + 1; j < n; j++) for (int k = j + 1; k < n; k++) {
			if (lens[i] + lens[j] > lens[k] && lens[j] + lens[k] > lens[i] && lens[k] + lens[i] > lens[j]) count++;
		}
		//出力
		Console.WriteLine(count);
	}
}