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));
  $l = explode(" ", trim(fgets(STDIN)));
  sort($l);
//   print_r($l);
  $cnt = 0;
  for($i=0; $i<$n; $i++){
      for($j=$i+1; $j<$n; $j++){
          $top = $j;
          $btm = $n;
          while($top+1 < $btm){
              $cen = intdiv($top+$btm,2);
              if($l[$i]+$l[$j] > $l[$cen]){
                  $top = $cen;
              }else{
                  $btm = $cen;
              }
          }
          $cnt += ($top-$j);
      }
  }
  echo $cnt;