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;

public class Main {
    static Scanner sc;
    public static void main(String[] args) {
        sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] A = new int[N];
        for(int i = 0; i < N; i++) {
            A[i] = sc.nextInt();
        }

        int ct = 0;
        for(int i = 0; i < N - 2; i++) {
            for(int j = i + 1; j < N - 1; j++) {
                for(int k = j + 1; k < N; k++) {
                    if(A[i] < A[j] + A[k] && A[j] < A[i] + A[k] && A[k] < A[i] + A[j]) {
                        ct += 1;
                    }
                }
            }
        }

        System.out.println(ct);
    }
}