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.Arrays;
import java.util.Scanner;

public class Main {
	private static Scanner sc;

	public static void main(String[] args) {
		sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] array = new int[n];

		for (int i = 0; i < n; i++) {
			array[i] = sc.nextInt();
		}

		Arrays.sort(array);
		int length = n;
		int count = 0;

		for (int i = 0; i < n - 2; i ++) {
			int max = array[length - 1];

			for (int j = 0; j < length - 1; j ++) {
				int hen1 = array[j];
				for (int k = 0; k < j; k ++) {
					int hen2 = array[k];
					if (hen1 + hen2 > max) {
						count += 1;
					}

				}
			}

			length -= 1;
		}

		System.out.println(count);
	}

}