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: Accepted)

<?php
fscanf(STDIN,"%d",$n);
$l_li = explode(" ",trim(fgets(STDIN)));

sort($l_li);

$c = 0;
$end = count($l_li)-1;
for($i=0;$i<$n-2;$i++){
  for($j=$i+1;$j<$n;$j++){
    $ab = $l_li[$i]+$l_li[$j];
    $start = $j;
    $end = count($l_li);
    
    while($start+1 < $end){
      $center = intdiv($start+$end,2);
      if($l_li[$center]<$ab){
        $start = $center;
      }else{
        $end = $center;
      }
    }
    
    $c += ($start - $j);
  }
}

echo $c;