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<cstdio>
#include<functional>
#include<algorithm>
#define MM	2100000000
using namespace std;
int main(void)
{
	int n,a[100],i,j,sum,mn,x;
	scanf("%d",&n);
	for(i=0;i<n;i++)	scanf("%d",&a[i]);
	mn=MM;
	for(i=-100;i<=100;i++)	{
		x=0;
		for(j=0;j<n;j++)	{
			x+=(i-a[j])*(i-a[j]);
		}
		mn=min(mn,x);
	}
	printf("%d\n",mn);
	return 0;
}