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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main{

	public static void main(String[] args) {

		Scanner scanner = new Scanner(System.in);


		int n = Integer.parseInt(scanner.nextLine());

		String[] temp = scanner.nextLine().split(" ");
		int[] list    = new int[n];

		for(int i = 0; i < n; i++) {
			list[i] = Integer.parseInt(temp[i]);
		}

		int count = 0;

		for(int i = 0; i < n - 2; i++) {
			for(int j = i + 1; j < n - 1; j++) {
				for(int k = j + 1; k < n; k++) {
					if(list[i] + list[j] > list[k] && list[k] + list[j] > list[i] && list[i] + list[k] > list[j]) {
						count++;
					}
				}
			}
		}

		System.out.println(count);

	}
}