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 Ruby (2.3.3) (judge verdict: Wrong Answer)

# N  個の整数 a1,a2,..,aN が与えられます。えび君はこれらを書き換えて全て同じ整数にしようとしています。
# 各ai(1≦i≦N)は高々一回しか書き換えられません(書き換えなくても良い)。
# 整数xを整数yに書き換えるとき、コストが(x−y)2かかります。
# 仮にai=aj(i≠j)だとしても、ひとつ分のコストで同時に書き換えることは出来ません(入出力例2 を参照)。
# えび君が目的を達成するのに必要なコストの総和の最小値を求めてください。

n = gets.to_i
a = gets.chomp.split
n.times do |i|
    a[i] = a[i].to_i
end

a_each_kinds = []
a.each do |num|
    if !a_each_kinds.include?(num)
        a_each_kinds << num
    end
end

if a_each_kinds.length == 1
    puts 0
else
    costs = []
    (0..100).each do |num|
        cost = 0
        n.times do |i|
            cost += (a[i] - num) ** 2
        end
        costs << cost
    end
    puts costs.min
end