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;
import java.util.ArrayList;
import java.util.List;

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        Integer N = Integer.parseInt(scanner.next());
        List<Integer> L = new ArrayList<>();
        
        for(int i = 0; i < N; i++) {
            L.add(Integer.parseInt(scanner.next()));
        }

        Integer count = 0;

        for(int i = 0; i < N; i++) {
            for(int j = i + 1; j < N; j++) {
                for(int k = j + 1; k < N; k++) {
                    int a = L.get(i);
                    int b = L.get(j);
                    int c = L.get(k);

                    if(Math.abs(b - c) < a && a < (b + c)) {
                        count++;
                    }
                }
            }
        }

        System.out.println(count);

        scanner.close();
    }
}