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.*;
public class Main {
    public static void main(String[] args) {
        //data input
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(sc.nextInt());
        }

        //sort
        list.sort(new Comparator<Integer>() {
            @Override
            public int compare(Integer o1, Integer o2) {
                return o1 - o2;
            }
        });

        //search
        long ct = 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 = list.get(i);
                    int b = list.get(j);
                    int c = list.get(k);
                    if (a < b + c && b < a + c && c < a + b) {
                        ct++;
                    } else {
                        break;
                    }
                }
            }
        }

        System.out.println(ct);

    }
}