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 <bits/stdc++.h>

using namespace std;

int main() {

	int n; scanf("%d", &n);

	vector<int> arr(n);

	for (int i = 0; i < n; i++)
		scanf("%d", &arr[i]);

	int m = 1e9;

	for (int i = -100; i <= 100; i++) {

		int cost = 0;

		for (int w : arr)
			cost += (w - i) * (w - i);

		m = min(m, cost);

	}

	printf("%d", m);

	return 0;

}