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 sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		int[] l = new int[n];
		for (int i = 0; i < n; i++) {
			l[i] = sc.nextInt();
		}
		
		int cnt=0;
		for (int a = 0; a < n-2; a++) {
			for (int b = a+1; b < n-1; b++) {
				for (int c = b+1; c < n; c++) {
					boolean ba = l[a] < l[b]  + l[c];
					boolean bb = l[b] < l[c]  + l[a];
					boolean bc = l[c] < l[a]  + l[b];
					if( ba && bb && bc ) {
						cnt++;
					}
				}
			}
		}
		
		System.out.println(cnt);
		
	}

}