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.*;
public class Main{
  public static void main(String[]args){
      Scanner sc = new Scanner(System.in);

      int N = sc.nextInt();
      int data[] = new int[N];

      int a = 0;
      int total=0;

      while(a<N){
        data[a] = sc.nextInt();
        a++;
      }

      Arrays.sort(data);

      for(int i = 0;i<N-2;i++){
        for(int j = i+1;j<N-1;j++){
          int low = 0;
          int high = N;
          int middle = 0;

          while(high-low>1){

              middle =(high+low)/2;

             
            if(data[middle]<data[i]+data[j]){
              low = middle;
              
            }else{
              high = middle;
          }
        }
        total=total+high-1-j;
      }


    }
    System.out.println(total);
  }
}