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;

class Program{
    static void Main(string[] args){
        
        int N = int.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        int[] a = new int[N];
        int sum = 0;
        for(int i=0;i<N;i++){ 
            a[i] = int.Parse(str[i]);
            sum += a[i];
        }
        
        int c1 = sum/N;
        int c2 = c1 + 1;
        
        int ans1=0, ans2=0;
        for(int i=0;i<N;i++){
            ans1 += (a[i]-c1)*(a[i]-c1);
            ans2 += (a[i]-c2)*(a[i]-c2);
        }
        
        
        Console.WriteLine(Math.Min(ans1, ans2));
    }
}