#include <bits/stdc++.h>
using namespace std;

int main(void) {
  int N; cin >> N;
  vector<int> a(N);
  for (int i = 0; i < N; i++) cin >> a.at(i);

  int c = (int)round((double)accumulate(a.begin(), a.end(), 0)/(double)N);
  int ret = 0;
  for (int a_i : a) ret += (a_i - c)*(a_i - c);
  cout << ret << endl;

  return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

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 <bits/stdc++.h>
using namespace std;

int main(void) {
  int N; cin >> N;
  vector<int> a(N);
  for (int i = 0; i < N; i++) cin >> a.at(i);

  int c = (int)round((double)accumulate(a.begin(), a.end(), 0)/(double)N);
  int ret = 0;
  for (int a_i : a) ret += (a_i - c)*(a_i - c);
  cout << ret << endl;

  return 0;
}

```