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: Accepted)

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[] xs =  new int[n];
        for (int i = 0; i < n; i++) {
            xs[i] = sc.nextInt();
        }
        Arrays.sort(xs);

        int count = 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++) {
                    if (xs[c] >= xs[a] + xs[b]) {
                        break;
                    }
                    if (xs[a] < xs[b] + xs[c] && xs[b] < xs[a] + xs[c]) {
                        count++;
                    }
                }
            }
        }

        System.out.println(count);
    }
}