Problem:
Score : 200 points

Problem Statement

Evi has N integers a_1,a_2,..,a_N. His objective is to have N equal integers by transforming some of them.

He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j), he has to pay the cost separately for transforming each of them (See Sample 2).

Find the minimum total cost to achieve his objective.

Constraints

1≦N≦100

-100≦a_i≦100

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum total cost to achieve Evi's objective.

Sample Input 1

2
4 8

Sample Output 1

8

Transforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.

Sample Input 2

3
1 1 3

Sample Output 2

3

Transforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.

Sample Input 3

3
4 2 5

Sample Output 3

5

Leaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.

Sample Input 4

4
-100 -100 -100 -100

Sample Output 4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io;

fn read_line<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn solve_c(a: &[i32]) -> i32 {
    let med: f64 = a.iter().fold(0, |acc, x| acc + x) as f64 / a.len() as f64;
    let med = med.round() as i32;
    a.iter().fold(0, |acc, x| acc + (x - med) * (x - med))
}

fn main() {
    let _ = read_line::<i32>();
    let input = read_line::<i32>();
    println!("{}", solve_c(&input));
}