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: Wrong Answer)

import java.util.Arrays;
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];
		int count = 0;

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

		Arrays.parallelSort(l);

		for(int i = n-1; i >= 2; i--) {
			if(i != n-1 && l[i] == l[i+1]) continue;

			B:for(int a = i-1; a >= 1; a--) {
				if(a != i-1 && l[a] == l[a+1]) continue;

				for(int b = a-1; b >= 0; b--) {
					if(b != a-1 && l[b] == l[b+1]) continue;

					if(l[i] < l[a]+l[b]) {
						count++;
						System.out.printf("%d %d %d%n", l[i], l[a],l[b]);
					}else {
						break B;
					}

				}
			}

		}

		System.out.println(count);

		sc.close();
	}
}