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: Wrong Answer)

<?php
fscanf(STDIN, "%d", $length);
for ($i = 0; $i < $length; $i++) {
    fscanf(STDIN, "%s", $array_number[]);
}
$result = 0;
$sum    = array_sum($array_number);
$max     = max($array_number);
$min_num = min($array_number);
$y      = 0;
$co_y   = 0;
$tmp_array  = array();
$result_tmp = array();
$min     = 0;
$item    = array();
for ($j = $min_num; $j <= $max; $j++) {
	$sum_tmp = 0;
	for ($i = 0; $i < $length; $i++) {
		$element = $array_number[$i];
		$sum_tmp += pow(($element - $j), 2);
	}
	$item['index']   = $j;
	$item['sum'] = $sum_tmp;
	$result_tmp[] = $item;
}

$min  = $result_tmp[0]['sum'];
$co_y = $result_tmp[0]['index'];
foreach($result_tmp as $compare_value) {
	if ($min > $compare_value['sum']) {
		$min = $compare_value['sum'];
		$co_y = $compare_value['index'];
	}
}

for ($i = 0; $i < $length; $i++) {
	$element = $array_number[$i];
	if ($element != $co_y) {
		$result += pow(($element - $co_y), 2);
	}
}

echo $result;

?>