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: Accepted)

def f(point, arr)
  result = arr.inject(0){|result, item|
    result + (item-point)**2
  }
  return result
end
def re(low, high, arr)
  return f(((high-low)/2)+low, arr) if high-low <= 2
  mid_left = ((low * 2) + high) / 3
  mid_right = (low + (high * 2)) / 3
  if f(mid_left, arr) >= f(mid_right, arr)
    re(mid_left, high, arr)
  else
    re(low, mid_right, arr)
  end
end
n = gets.chop.to_i
arr = gets.chop.split.map(&:to_i)

print re(arr.min, arr.max, arr)