Problem:
Score : 300 points

Problem Statement

There are N people living on a number line.

The i-th person lives at coordinate X_i.

You are going to hold a meeting that all N people have to attend.

The meeting can be held at any integer coordinate. If you choose to hold the meeting at coordinate P, the i-th person will spend (X_i - P)^2 points of stamina to attend the meeting.

Find the minimum total points of stamina the N people have to spend.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq X_i \leq 100

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print the minimum total stamina the N people have to spend.

Sample Input 1

2
1 4

Sample Output 1

5

Assume the meeting is held at coordinate 2. In this case, the first person will spend (1 - 2)^2 points of stamina, and the second person will spend (4 - 2)^2 = 4 points of stamina, for a total of 5 points of stamina. This is the minimum total stamina that the 2 people have to spend.

Note that you can hold the meeting only at an integer coordinate.

Sample Input 2

7
14 14 2 13 56 2 37

Sample Output 2

2354

Solution in Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
	val N = scala.io.StdIn.readInt
	val X = scala.io.StdIn.readLine.split(" ").map(_.toInt)

	val sum1 = X.map(z => z*z).sum
	val sum2 = X.sum

	if(sum2%N == 0) println(sum1 - sum2*sum2/N)
	else{
		val p1 = sum2/N
		val p2 = (sum2 + N - 1)/N

		println(math.min(N*p1*p1 - 2 * sum2 * p1 + sum1, N*p2*p2 - 2*sum2*p2 + sum1))
	}
}