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<cmath>

using namespace std;

int main()
{	
	long long n, i, a[110], res = 0;
	double m,sum=0;
	cin >> n;
	for (i = 0; i < n; i++) {
		cin >> a[i];
		sum += a[i];
	}
	
	m = round(sum / n);
	for (i = 0; i < n; i++) {
		res += pow((a[i] - m), 2);
	}
	
	cout << res << endl;
	return 0;
}