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 <vector>

int main()
{
	int N; std::cin >> N;
	int sum = 0;
	std::vector<int> a(N);
	for(auto &x: a)
	{
		std::cin >> x;
		sum += x;
	}
	int X = sum/N + ((double)sum/N-sum/N>0.5 ? 1 : 0);
	int ans = 0;
	for(const auto &z: a) ans += (X-z)*(X-z);
	std::cout << ans << std::endl;
	return 0;
}