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 Perl (v5.18.2) (judge verdict: Accepted)

use strict;
my $N = <STDIN>;
my $line = <STDIN>;
my @a=split ' ',$line;

my $mean=0;
for(my $i=0;$i<$N;$i++){ $mean += $a[$i]; }

$mean = int($mean/$N);

my @cost;
my $l=0;
my $plus=$mean;
my $minus=$mean;
my $tempM=$mean;
my $tempP=$mean;

while($l<3){
  my $k=0;
  my $up=0;
  my $down=0;
  while($k<$N){
    $up += ($a[$k]-$tempP)*($a[$k]-$tempP);
    $k++;
  }
  my $k=0;
  while($k<$N){
    $down += ($a[$k]-$tempM)*($a[$k]-$tempM);
    $k++;
  }
  push @cost,$up;
  push @cost,$down;
  $tempP++;
  $tempM--;
  $l++;
}

@cost = sort{$a<=>$b}@cost;

print"$cost[0]\n";