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::io::prelude::*;
use std::cmp;

fn run(args: &Vec<String>) -> i32 {
    let n: i32 = args[0].parse().unwrap();
    let ai: Vec<i32> = args[1].split(' ').map(|s| s.parse().unwrap()).collect();
    let ave = ai.iter().fold(0, |a, b| a + b) / n;

    let a1 = sum(&ai, ave - 1);
    let a2 = sum(&ai, ave);
    let a3 = sum(&ai, ave + 1);

    cmp::min(cmp::min(a1, a2), a3)
}

fn sum(ai: &Vec<i32>, v: i32) -> i32 {
    ai.into_iter().fold(0, |a, b| a + (b - v) * (b - v))
}

fn main() {
    let stdin = io::stdin();
    let args = stdin.lock().lines().map(|l| l.unwrap()).collect();
    let r = run(&args);
    println!("{}", r);
}