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.Linq;

public class Test
{
	public static void Main()
	{
		// your code goes here
		
		int n = int.Parse(Console.ReadLine());
		var l = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
		int counter = 0;
		
		for(int a=0;a!=n-2;a++){
			for(int b=a+1;b!=n-1;b++){
				for(int c=a+2;c!=n;c++){
					if(l[a]<l[b]+l[c]){
						if(l[b]<l[c]+l[a]){
							if(l[c]<l[a]+l[b]){
								counter++;
							}
						}
					}
				}
			}
		}
		
		Console.WriteLine(counter);
		
	}
}