Contest: Task: Related: TaskB

Score : $200$ points

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.

- $1≦N≦100$
- $-100≦a_i≦100$

The input is given from Standard Input in the following format:

$N$ $a_1$ $a_2$ ... $a_N$

Print the minimum total cost to achieve Evi's objective.

2 4 8

8

Transforming the both into $6$s will cost $(4-6)^2+(8-6)^2=8$ dollars, which is the minimum.

3 1 1 3

3

Transforming the all into $2$s 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 $1$s.

3 4 2 5

5

Leaving the $4$ as it is and transforming the $2$ and the $5$ into $4$s will achieve the total cost of $(2-4)^2+(5-4)^2=5$ dollars, which is the minimum.

4 -100 -100 -100 -100

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is $0$.