#include <algorithm>
#include <climits>
#include <iostream>
#include <vector>
using namespace std;

int main() {
	int ans = INT_MAX, sum;
	size_t N;
	cin >> N;
	vector<int> a(N);
	for (auto& x : a) cin >> x;
	for (int i = -100; i <= 100; ++i) {
		sum = 0;
		for (auto&x : a) sum += (x - i) * (x - i);
		ans = min(ans, sum);
	}
	cout << ans;
}
### Prompt

Develop a solution in cpp to the problem described below:

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

### Response

```cpp
#include <algorithm>
#include <climits>
#include <iostream>
#include <vector>
using namespace std;

int main() {
	int ans = INT_MAX, sum;
	size_t N;
	cin >> N;
	vector<int> a(N);
	for (auto& x : a) cin >> x;
	for (int i = -100; i <= 100; ++i) {
		sum = 0;
		for (auto&x : a) sum += (x - i) * (x - i);
		ans = min(ans, sum);
	}
	cout << ans;
}
```