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: Wrong Answer)

<?php
$n = int();
$lArray = ints();
sort($lArray);
//echo implode(" ", $lArray),"\n";
$c = 0;
for($i = 2; $i < $n; $i++){
  for($j = 1; $j < $i; $j++){
    $min = $lArray[$i] - $lArray[$j];
    
    $k = bsl($lArray, $min);
    $add = $j - $k - 1;
    $c+=max($add,0);
//    echo $lArray[$i]," ",$lArray[$j]," ",$min," ",$add," j=$j k=$k add=$add\n";
  }
}
echo $c;
function mbsl($nums, $target){
  static $map;
  if(!isset($map[$target])){
    $map[$target] = bsl($nums, $target);
  }
  return $map[$target];
}
function bsl($nums, $target) {
    $size = count($nums);
    $min = 0; 
    $max = $size - 1;
    while(true){
        $center = floor(($min + $max) / 2);
        $centerValue = $nums[$center];
        if($target == $centerValue){
            return $center;
        }elseif($target > $centerValue){
            $min = $center + 1;
        }else{
            $max = $center;
        }
        if($min == $max){
            $center = floor(($min + $max) / 2);
            $centerValue = $nums[$center];
            if($centerValue == $target){
                return $center;
            }elseif($centerValue < $target){
                return $center;
            }else{
                return $center-1;
            }
        }
    }
}
function ints(){
  return array_map("intval", explode(" ", trim(fgets(STDIN))));
}
function int(){
  return intval(trim(fgets(STDIN)));
}