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 OCaml (4.02.3) (judge verdict: Accepted)

open Batteries
open BatPrintf

let scan fmt f =
  Scanf.sscanf (read_line ()) fmt f

let scan_list cnv =
  read_line ()
  |> String.split_on_char ' '
  |> List.map cnv

let scan_listn n cnv =
  (0 --^ n) |> Enum.map (fun _ -> (cnv % read_line) ())

let bsearch_ge arr a =
  let l = Array.length arr in
  match Array.bsearch Int.ord arr a with
  | `All_lower -> l
  | `All_bigger -> 0
  | `Just_after n -> l - n -1
  | `At n -> l - n
  | `Empty -> 0

let rec zip xs ys =
  match xs, ys with
  | [], _ -> []
  | _, [] -> []
  | x::xs, y::ys ->
    (x, y) :: zip xs ys

let n = scan "%d" identity
let xs = scan_list Int.of_string

let () =
  let half = (List.sum xs) / n in
  let half2 = (List.sum xs) / n + 1 in
  let n = List.sum @@ List.map (fun n -> let k = n - half in k*k) xs in
  let m = List.sum @@ List.map (fun n -> let k = n - half2 in k*k) xs in
  printf "%d" @@ min n m