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
$n=trim(fgets(STDIN));
$l=explode(" ",trim(fgets(STDIN)));
$i=0;
rsort($l);
$ans=0;
while($i<$n-2){
  $j=$i+1;
  while($j<$n-1){
    $k=$j+1;
    while($k<$n){
      if($l[$i]<$l[$j]+$l[$k]){
        ++$ans;
      }else{
        $k=$n-1;
      }
      ++$k;
    }
    if($l[$i]>=$l[$j]+$l[$j+1]){
      $j=$n-2;
    }
    ++$j;
  }
  ++$i;
}
echo $ans;