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C - Be Together

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.

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 $0$.