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: Accepted)

<?php
$n = intval(fgets(STDIN));
$lArray = array_map("intval", explode(" ", trim(fgets(STDIN))));
sort($lArray);
//echo implode(" ", $lArray),"\n";
$map = [];
for($i = 1; $i <= 2000; $i++){
  $map[$i] = 0;
}
foreach($lArray as $l){
  $map[$l]++;
}
$sum = 0;
for($i = 1; $i <= 2000; $i++){
  $sum+=$map[$i];
  $accum[$i] = $sum;
}

$c = 0;
for($i = 0; $i < $n - 1; $i++){
  for($j = 0; $j < $i; $j++){
    $add = $accum[$lArray[$i] + $lArray[$j] - 1] - ($i + 1);
    $c+=max(0,$add);
//    echo "i=$i j=$j {$lArray[$i]} {$lArray[$j]} ".($lArray[$i]+$lArray[$j])."  add=$add\n";
  }
}
echo $c;