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.stream.Stream;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.nextLine());
        String str  = sc.nextLine();
        String[] astr = str.split(" "); //状況に合わせて
        int[] in_data = Stream.of(astr).mapToInt(x->{
            try{
                return Integer.parseInt(x);
            }
            catch(Exception e){
                e.printStackTrace();
            }
            return 0;
        }).toArray();
        sc.close();
        List<Integer> data = new ArrayList<Integer>(in_data.length);
        for (int i = 0; i < in_data.length; i++) {
            data.add(in_data[i]);
        }
        data.sort(Comparator.reverseOrder());
        //System.out.println(data);

        int ans =0;
        Boolean flag = false;

        for(int i =0;i< data.size() ;i++){
            for(int j = i+1;j<data.size();j++){
                    if(i > 2*j){
                        break;
                    }
                for(int k =j+1;k<data.size();k++){
                    flag = check(data.get(i),data.get(j),data.get(k));
                    if(flag == true){
                        ans +=1;
                    }
                }
            }
        }
        System.out.println(ans);
    }

    public static Boolean check(Integer a, Integer b, Integer c){
        if(a < b + c && b < a + c &&  c < a + b){
            return  true;
        }
        else{
            return  false;
        }
    }

}