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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
  $n = trim(fgets(STDIN));
  $l = explode(" ", trim(fgets(STDIN)));
  $cnt = 0;
  for($x=0; $x<$n; $x++){
      for($y=$x+1; $y<$n; $y++){
          for($z=$y+1; $z<$n;$z++){
              if($l[$x] < $l[$y]+$l[$z] 
              && $l[$y] < $l[$x]+$l[$z]
              && $l[$z] < $l[$x]+$l[$y]){
                  $cnt++;
              }
          }
      }
  }
  echo $cnt;