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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program sample
	implicit none
    integer(8) :: N,i,count,average,sum1
    integer(8),allocatable :: x(:),a(:),b(:)
    real(8) :: count2,average2
    
    read(*,*) N
    
    allocate(x(N))
    allocate(b(N))
    
    
    read(*,*) x
    
    !write(*,*) x
    
    count =0
    count2=0
    do i=1,N
    	b(i) = x(i)-x(1)
        count = count +x(i)
        count2= count2 +real(x(i))
    end do
    
    average = count / N
    average2 = count2 /N
    
    sum1= 0
    if (maxval(b) ==minval(b)) then
    	write(*,*) 0
    else if (abs(average2-average) >= abs(average2-average-1) ) then
    	do i=1,N
        	sum1= sum1 + (x(i)-average-1)**2
        end do
        write(*,*) sum1
    else
    	do i=1,N
        	sum1 = sum1 + (x(i)-average) **2
    	end do
    	write(*,*) sum1
    end if
    
	deallocate(x)
    stop
end program sample