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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(arg: Array<String>) {
    val N = nextInt()
    val X = listOfInt().toIntArray()
    val sum = X.sum()
    val av1 = sum / N
    val av2 = av1 + 1
    val ans1 = X.sumBy { (av1 - it) * (av1 - it) }
    val ans2 = X.sumBy { (av2 - it) * (av2 - it) }
    val ans = Math.min(ans1, ans2)
    println(ans)
}

fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfLong() = listOfString().map(String::toLong)
fun listOfInt(delta: Int = 0) = listOfString().map { Integer.parseInt(it) + delta }