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.*;
import java.io.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        //BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        //StringTokenizer st = new StringTokenizer(br.readLine());
        //PrintWriter pw = new PrintWriter("Main.out");

        int n = sc.nextInt();
        int[] sticks = new int[n];
        for(int i = 0; i<n; i++){
            sticks[i] = sc.nextInt();
        }
        int diff = 0;
        loop : for(int i = 0; i<n; i++){
            for(int j = i+1; j<n; j++){
                for(int k = j+1; k<n; k++){
                    if(triangle(sticks[i], sticks[j], sticks[k])){
                        diff++;
                        //continue loop;
                    }
                }
            }
        }
        System.out.println(diff);
    }

    public static boolean triangle(int a, int b, int c){
        if(a + b > c && a + c > b && b + c > a){
            return true;
        }
        return false;
    }
}