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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.IntSummaryStatistics;
import java.util.Scanner;

class Solver {
	static final Solver INSTANCE = new Solver();

	void solve(Scanner sc) {
		int N = sc.nextInt();
		int[] X = new int[N];
		for (int i = 0; i < N; i++) {
			X[i] = sc.nextInt();
		}
		IntSummaryStatistics statistics = Arrays.stream(X).summaryStatistics();
		long ceil = (long) Math.ceil(statistics.getAverage());
		long floor = (long) Math.floor(statistics.getAverage());
		long ceilSum = 0;
		long floorSum = 0;
		for (int i = 0; i < N; i++) {
			long C = X[i] - ceil;
			ceilSum += C * C;
			long F = X[i] - floor;
			floorSum += F *F;
		}

		System.out.println(Math.min(ceilSum, floorSum));
	}
}

class Main {
	public static void main(String... args) {
		Scanner in = new Scanner(System.in);

		Solver.INSTANCE.solve(in);

		in.close();
	}
}