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 BeTogether
{
	static void Main(String[] args)
	{
		int N;
		int[] a;
		String[] vals;

		N = int.Parse(Console.ReadLine());
		a = new int[N];
		vals = Console.ReadLine().Split(' ');
		for(int i=0; i<N; i++)
			a[i] = int.Parse(vals[i]);
		int min = 101;
		int max = -101;
		for(int i=0; i<N; i++)
		{
			if(min > a[i])
				min = a[i];
			if(max < a[i])
				max = a[i];
		}
		if(min == max)
		{
			Console.WriteLine(0);
			return;
		}
		int minCost = int.MaxValue;
		int cost;
		for(int v=min; v<=max; v++)
		{
			cost=0;
			for(int i=0; i<N; i++)
				cost += (a[i]-v)*(a[i]-v);
			if(minCost > cost)
				minCost = cost;
		}
		Console.WriteLine(minCost);
	}
}