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;

int main(void){
	long long s=0, t=0, n, a, ans=0;
 	cin >> n;
	for(int i=0; i<n; i++){
		cin >> a;
		s += a;
		t += a*a;
	}
	a = s/n;
	if(s%n==0) ans = t - s*s/n;
	else ans = min(n*a*a-2*s*a+t, n*(a+1)*(a+1)-2*s*(a+1)+t);
	cout << ans << endl;
}