Problem:
Score : 200 points

Problem Statement

Evi has N integers a_1,a_2,..,a_N. His objective is to have N equal integers by transforming some of them.

He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j), he has to pay the cost separately for transforming each of them (See Sample 2).

Find the minimum total cost to achieve his objective.

Constraints

1≦N≦100

-100≦a_i≦100

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum total cost to achieve Evi's objective.

Sample Input 1

2
4 8

Sample Output 1

8

Transforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.

Sample Input 2

3
1 1 3

Sample Output 2

3

Transforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.

Sample Input 3

3
4 2 5

Sample Output 3

5

Leaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.

Sample Input 4

4
-100 -100 -100 -100

Sample Output 4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.

Solution in PHP (5.6.30) (judge verdict: Accepted)

<?php
error_reporting(0);
$stdin = file_get_contents('php://stdin');
$line = explode("\n",$stdin);
$fi = 0;
$cnt = 0;
$list = array();
$key = new stdclass();
foreach($line as $l) {
  if (empty($l)) continue;
  if ($fi == 0) {
    $a = explode(" ",$l);
    $key->N = $a[0];
    $fi++;
    continue;
  }
  if ($fi > 0) {
    $a = explode(" ",$l);
    $key->A=$a;
  }
}
$m = max($key->A);
$n = min($key->A);
if ($m == $n) {
  printf("0\n");
  exit;
}
$cost = 99999999;
for($i=$n;$i<=$m;$i++) {
  $cost = min(getcost($i,$key->A),$cost);
}
printf("%d\n",$cost);
function getcost($i,$a) {
  $res = 0;
  foreach($a as $n) {
    $res += pow(($n-$i),2);
  }
  return $res;
}