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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
//error_reporting(0);
$N = trim(fgets(STDIN));
//list($A,$B) =  explode(" ",trim(fgets(STDIN)));
$l = explode(" ",trim(fgets(STDIN)));

rsort($l);
$tot = 0;
for($i=0;$i<$N;$i++) {
  for($j=$i+1;$j<$N;$j++) {
    if ($i==$j) continue;
    for($k=$j+1;$k<$N;$k++) {
      $a = $l[$i];
      $b = $l[$j];
      $c = $l[$k];
      if (numtriangle($a,$b,$c)==0) break 2;
      $tot+=1;
    }
  }
}
printf("%d\n",$tot);

function numtriangle($a,$b,$c) {
  $ret = 0;
  $m = min($a,$b,$c);
  if ($a < $b + $c) {
    if ($b < $c + $a) {
      if ($c < $a + $b) {
        $ret= 1;
      }
    }
  }
 // printf("%d %d %d %d\n",$a,$b,$c,$ret);
  return $ret;
}