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 LuaJIT (2.0.4) (judge verdict: Accepted)

function pointsOfStamina(p, x)
   local points = 0
   for i = 1, #x do
      points = points + (x[i] - p)^2
   end
   return points
end


local n = io.read("*n")
local x = {}

for i = 1, n do
   x[i] = io.read("*n")
end

local min = {coordinate=1, points=pointsOfStamina(1, x)}
for i = 2, 100 do
   local points = pointsOfStamina(i, x)
   if points < min.points then
      min.coordinate = i
      min.points = points
   end
end

print(string.format("%d", min.points))