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::str::FromStr;
use std::str::Chars;
use std::i32;
use std::u8;
use std::f64;
use std::ascii::AsciiExt;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::BTreeMap;
use std::collections::BTreeSet;
use std::collections::VecDeque;
use std::io::prelude::*;
use std::time::Duration;
use std::cmp;

macro_rules! println_stderr(
    ($($arg:tt)*) => { {
        let r = writeln!(&mut ::std::io::stderr(), $($arg)*);
        r.expect("failed printing to stderr");
    } }
);

macro_rules! print_stderr(
    ($($arg:tt)*) => { {
        let r = write!(&mut ::std::io::stderr(), $($arg)*);
        r.expect("failed printing to stderr");
    } }
);

fn main() {
    let n = next_int();
    let a = next_ints();
    let mut ans = 1e8 as i64;
    for i in -100..101 {
        let mut cost = 0;
        for e in a.clone() {
            cost += (e-i).pow(2);
        }
        ans = cmp::min(ans,cost);
    }
    println!("{}",ans);
}

#[allow(dead_code)]
fn next_string() -> String {
    let mut input = String::new();
    io::stdin().read_line(&mut input).unwrap();
    input
}

#[allow(dead_code)]
fn next_strings() -> Vec<String> {
    let input = next_string();
    input.split_whitespace().map(|x| x.parse().unwrap()).collect()
}

#[allow(dead_code)]
fn next_int() -> i64 {
    let input = next_string();
    i64::from_str(input.trim()).unwrap()
}

#[allow(dead_code)]
fn next_ints() -> Vec<i64> {
    let input = next_string();
    input.split_whitespace().map(|x| x.parse().unwrap()).collect()
}