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 nums = sc.nextInt();
        int sum = 0;
        int[] list = new int[nums];
        for(int i = 0; i < nums; i++){
            int num =  sc.nextInt();
            list[i]= num;
        }
        Arrays.sort(list);
        for(int k = 0; k < list.length; k++){
            int a = list[k];
            for (int i = k+1; i < list.length ; i++) {
                int b = list[i];
                for (int j = i+1; j < list.length; j++) {
                   int c = list[j];
                   if(c < a + b){
                       sum++;
                   }else{
                       break;
                   }
                }
            }
        }
        System.out.println(sum);
    }
}