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 Ruby (2.3.3) (judge verdict: Wrong Answer)

attrs = $stdin.read.split("\n")

num = attrs[0]

x_cors = attrs[1].split(' ').map(&:to_i)

min = x_cors.map { |num| num * num }.inject(:+)
pre_min = min + 1
p = 1

while pre_min > min do
  pre_min = min
  min = x_cors.map { |num| num * num }.inject(:+) - 2 * p * x_cors.inject(:+) + x_cors.length * p * p

  # puts "p: #{p}, min: #{min}, pre_min: #{pre_min}"
  p += 1
end

puts min