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)

fn main() {
    let n: usize = {
        let mut buffer = String::new();
        std::io::stdin().read_line(&mut buffer).unwrap();

        buffer.trim().parse().unwrap()
    };

    let nums: Vec<isize> = {
        let mut buffer = String::new();
        std::io::stdin().read_line(&mut buffer).unwrap();

        buffer.split_whitespace().map(|i|i.parse().unwrap()).collect()
    };

    assert_eq!(n, nums.len());

    let mut avg = 0.0;
    for i in nums.clone() {
        avg += i as f32 / n as f32;
    }
    let avg = avg.round() as isize;

    let mut sum = 0;
    for i in nums.clone() {
        sum += (avg - i).abs().pow(2);
    }
    let sum = sum;

    println!("{:?}", sum);
}