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() {
int n;
int a[113];
cin >> n;
for (int i = 0; i < n; i++) cin >> a[i];
for(int x = -100; x <= 100; x++){
int current_cost = 0;
for(int i=0;i<n;i++) {
current_cost += (x - a[i]) * (x - a[i]);
}
a[112] = min(a[112],current_cost+4000000-2147483647);
}
cout << a[112] - 4000000 + 2147483647 << endl;
}