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: Runtime Error)

open Batteries

let rec solver p lst =
        match lst with
                  [] -> 0
                | first :: rest -> 
                        ((first - p) * (first - p)) + (solver p rest)

let rec solver2 n m lst = 
        if m = (n + 1) then
                solver n lst
        else
                let p = (n + m) / 2 in
                let lp = (n + p) / 2 in
                let rp = (p + 1 + m) / 2 in
                let lsum = solver lp lst in
                let rsum = solver rp lst in
                        if lsum < rsum then
                                solver2 n p lst 
                        else
                                solver2 (p + 1) m lst 

let lst = Scanf.scanf "%d\n" (
        fun n -> 
                Str.split (Str.regexp " ") (read_line ()) 
                |> List.map int_of_string
)

let () = 
        let minlst = List.min lst in
        let maxlst = List.max lst in
                solver2 minlst maxlst lst 
                |> Printf.printf "%d\n"