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.Arrays;
import java.util.Scanner;

public class Main {
    public static void debug(String str) {
        System.out.println(str);
    }

    public static void main(String[] args) {

        int N;
        long[] Ln;

        try (Scanner sc = new Scanner(System.in)) {
            N = sc.nextInt();
            Ln = new long[N];
            for (int i = 0; i < Ln.length; i++) {
                Ln[i] = sc.nextLong();
            }

        }
        long result2 =0;
        for (int i = 0; i < Ln.length; i++) {
            for (int j = i+1; j < Ln.length; j++) {
                for (int j2 = j+1; j2 < Ln.length; j2++) {
                    if(isTri(Ln[i], Ln[j], Ln[j2])){
                        result2++;
                    }
                }
            }
        }
        System.out.println(result2);

    }

    private static boolean isTri(long a,long b,long c){
        long[] arr = new long[]{a,b,c};
        Arrays.sort(arr);
        if(arr[0] + arr[1] > arr[2]){
            return true;
        }else{
            return false;
        }
    }


}