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.

Examples

Input

2
4 8


Output

8


Input

3
1 1 3


Output

3


Input

3
4 2 5


Output

5


Input

4
-100 -100 -100 -100


Output

0
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;

int main()
{
	int N;
	int a[110]={};
	int tmp,ans=1e7;
	
	cin >> N;
	for(int i=0;i<N;i++)
	{
		cin >> a[i];
	}
	
	for(int i=-100;i<=100;i++)
	{
		tmp=0;
		for(int j=0;j<N;j++)
		{
			tmp+=((i-a[j])*(i-a[j]));
		}
		ans=min(ans,tmp);
	}
	cout << ans << endl;
	return 0;
}