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 Java (OpenJDK 11.0.6) (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[] l = new int[n];
    for (int i = 0;i<n ;i++ ) {
      l[i] = sc.nextInt();
    }
    Arrays.sort(l);
    int count = 0;
    for(int i = n-1;i>1;i--){
      for(int j = i-1;j>0;j--){
        int a = BinarySearch(l,l[i]-l[j]+1);
        if(a < j){
          count += j - a;
        }
      }
    }
    System.out.println(count);
  }

  public static int BinarySearch(int a[] , int target){
    int left = -1;
    int right = a.length;
    while(right - left > 1){
      int mid = left + (right - left) / 2;
      if(a[mid] >= target){
        right = mid;
      }else{
        left = mid;
      }
    }
    return right;
  }

}