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;
use std::cmp;

fn cost_for(a: i32, numbers: &Vec<i32>) -> i32 {
    let mut cost = 0;
    for i in numbers {
        cost += (i - a).pow(2);
    }
    cost
}

fn min_cost(numbers: &Vec<i32>) -> i32 {
    let mut min_cost = std::i32::MAX;
    for i in (-100)..101 {
        min_cost = cmp::min(min_cost, cost_for(i, numbers));
    }
    min_cost
}

fn main() {
    let mut input = String::new();
    io::stdin().read_line(&mut input).unwrap();
    let mut iter = input.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();

    let mut numbers = Vec::with_capacity(n);
    let mut line = String::new();
    io::stdin().read_line(&mut line).unwrap();
    for token in line.split_whitespace() {
        numbers.push(token.parse().unwrap());
    }
    println!("{}", min_cost(&numbers));
}