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: Wrong Answer)

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

public class Main{
  public static void main(String args[]) throws IOException{
    Scanner s=new Scanner(System.in);
    int n=s.nextInt();
    
    int A[]=new int[n];
    
    for(int i=0;i<n-1;i++)
        A[i]=s.nextInt();
     Arrays.sort(A);
     
     
      int count = 0; 
  
    for (int i = n - 1; i >= 1; i--) 
    { 
        int l = 0, r = i - 1; 
        while (l < r) 
        { 
            if (A[l] + A[r] > A[i]) 
            { 
  
                // If it is possible with a[l], a[r] 
                // and a[i] then it is also possible 
                // with a[l+1]..a[r-1],a[r] and a[i] 
                count += r - l; 
  
                //checking for more possible solutions 
                r--; 
            }  
            else // if not possible check for  
                 // higher values of arr[l] 
            { 
                l++; 
            } 
        } 
    } 
   
    System.out.println(count);
  }
}