#include<bits/stdc++.h>
using namespace std;
vector<int> a;
int main () {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n,avg=0,total= 0;
  cin >> n;
  a.resize(n);
  for (auto &i : a) cin >> i, avg += i;
  avg = round(avg*1.0/n);
  for (int i : a) total += (i-avg)*(i-avg);
  cout << total << '\n';
  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;
vector<int> a;
int main () {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n,avg=0,total= 0;
  cin >> n;
  a.resize(n);
  for (auto &i : a) cin >> i, avg += i;
  avg = round(avg*1.0/n);
  for (int i : a) total += (i-avg)*(i-avg);
  cout << total << '\n';
  return 0;
}

```