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 Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
A = list(map(int, input().split()))

ans = 0
if min(A)==max(A):
    pass
else:
    import statistics
    th_mean = statistics.mean(A)
    th_median = statistics.median(A)
    if th_mean==th_median:
        for i in range(N):
            ans += (A[i]-th_mean)**2
    else:
        if th_mean>th_median:
            th_max = int((th_mean+0.5)//1)
            th_min = int(th_median)
        else:
            th_max = int((th_median+0.5)//1)
            th_min = int(th_mean)
            
        ans = 1000000
        for i in range(th_min, th_max+1):
            ans_temp = 0
            for j in range(N):
                ans_temp += (A[j]-i)**2
            if ans_temp < ans:
                th = i
                ans = ans_temp
print(ans)