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>
using namespace std;
#include<cstring>
int main()
{
	int a[105];
	int n;
	int sum=0;
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%d",&a[i]);
		sum+=a[i];
	}
	double avi=sum*1.0/n;
	int ne=avi;
	if(avi-ne>=0.5)
	ne++;
	int ans=0;
	for(int i=0;i<n;i++)
	ans+=(a[i]-ne)*(a[i]-ne);
	printf("%d",ans);
	return 0;	
}