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 = trim(fgets(STDIN));
$l = explode(" ", trim(fgets(STDIN)));

$ans = 0;
for ($mask = 0; $mask < (1 << $n); $mask++) {
     if(substr_count(decbin($mask), "1") !== 3) continue;
     
     $tri = [];
     for ($i = 0; $i < $n; $i++) {
          if(($mask >> $i) & 1) {
              $tri[] = $l[$i];
          }
     }
     
     if(count($tri) !== 3) continue;
     
     $check = false;
     if($tri[0]+$tri[1] > $tri[2] && $tri[0]+$tri[2] > $tri[1] && $tri[1]+$tri[2] > $tri[0]) {
         $ans++;
     }
}

echo $ans;