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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$N = trim(fgets(STDIN));
$a = explode(" ", trim(fgets(STDIN)));

$max = max($a);
$min = min($a);

$mid = floor(($max + $min) / 2);

while (true) {
    $val = sum($mid);
    $r = sum($mid + 1);
    $l = sum($mid - 1);

    if (min($val, $r, $l) == $val) {
        $ans = $val;
        break;
    } elseif ($val < $r) {
        $max = $mid;
        $mid = ceil(($min + $mid) / 2);
    } else {
        $min = $mid;
        $mid = floor(($max + $mid) /2);
    }
}

echo $ans;

function sum($n)
{
    global $a;
    $sum = 0;
    foreach ($a as $v) {
        $sum += ($v - $n) * ($v - $n);
    }
    return $sum;
}