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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;
class Simple {
    private int N;
    private int[] a;
    void Solve() {
        //input
        N = io.Int;
        a = new int[N];
        for(int i = 0; i < N; ++i) a[i] = io.Int;
        //cal
        var ave = (int)a.Average();
        int ta = 0, tb = 0;
        for(int i = 0; i < N; ++i) ta += (a[i] - ave) * (a[i] - ave);
        ave++;
        for(int i = 0; i < N; ++i) tb += (a[i] - ave) * (a[i] - ave);
        //ret
        Console.WriteLine(Math.Min(ta, tb));
    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Simple().Stream();
    void Stream() {
        Solve();
        io.writeFlush();
    }
}
class SimpleIO {
    string[] nextBuffer;
    int BufferCnt;
    char[] cs = new char[] {' '};
    StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
    public SimpleIO() {
        nextBuffer = new string[0];
        BufferCnt = 0;
        Console.SetOut(sw);
    }
    public string Next() {
        if(BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
        string st = Console.ReadLine();
        while(st == "") st = Console.ReadLine();
        nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        BufferCnt = 0;
        return nextBuffer[BufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void writeFlush() { Console.Out.Flush(); }
}