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: Accepted)

import java.util.*;
import java.io.*;
import java.lang.*;

public class Main{

public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        StringBuilder sb=new StringBuilder();
       int n=s.nextInt();
       int[] arr=new int[n];
       for(int i=0;i<n;i++){arr[i]=s.nextInt();}
       	Arrays.sort(arr);
       long count=0;
        for(int h=0;h<n-2;h++){
            int k1=h+2;
            for(int j=h+1;j<n-1;j++){
                while(k1<n &&arr[h]+arr[j]>arr[k1]){
                    k1++;
                }
                if(k1>j){count+=k1-j-1;}
            }
        }
       	
       System.out.println(count); 
    }
}