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 {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] sticks = new int[N];

        for(int i = 0; i < N; i++) {

            sticks[i] = Integer.parseInt(sc.next());
        }

        sc.close();

        int 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++) {

                    if(sticks[i] < sticks[j] + sticks[k] &&
                            sticks[j] < sticks[i] + sticks[k] &&
                                sticks[k] < sticks[i] + sticks[j]) {

                        count++;
                    }

                }
            }
        }

        System.out.println(count);
    }

}