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 Scala (2.11.7) (judge verdict: Wrong Answer)

  // C - いっしょ / Be Together https://atcoder.jp/contests/abc043/tasks/arc059_a

  import io.Source

  object Main extends App {
    val xs = Source.stdin.getLines()
    val n = xs.next().toInt
    val ns = xs.next().split(' ').map(_.toInt)

    println(solve(ns))
    
    def solve(ns: Seq[Int]): String = {
      // 平均かその前後の値に書き換えるのが一番いいはず
      val nss = ns.sorted
      val min = nss.min
      val max = nss.max
      // 平均で計算
      val a = (min + max) / 2
      var ans = cost(a, nss)
      // 1つ前の値で計算
      val pi = nss.lastIndexWhere(_ < a)
      if (pi >= 0) {
        ans = Math.min(cost(ns(pi), nss), ans)
      }
      // 1つ後の値で計算
      val ni = nss.indexWhere(_ > a)
      if (ni >= 0) {
        ans = Math.min(cost(ns(ni), nss), ans)
      }
      ans.toString
    }

    def cost(n: Int, ns: Seq[Int]): Int = {
      ns.map(m => Math.pow(m - n, 2).toInt).sum
    }
  }