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<cstring>
using namespace std;
int main()
{
int a[106];
int n,sum=0,ans=0;
cin>>n;
for(int i=1;i<=n;i++)
{
cin>>a[i];
sum+=a[i];
}
double n1=1.0*sum/n;
int av;
if(n1>=0)
av=(int)(n1+0.5);
else
av=(int)(n1-0.5);
for(int i=1;i<=n;i++)
{
	ans+=(a[i]-av)*(a[i]-av);
}
//cout<<sum<<" "<<n1<<" "<<av<<endl;
cout<<ans<<endl;
}
