#include<bits/stdc++.h>
using namespace std;
int main(){
  int m,j,y=0,z,w,t=0;
  cin>>m;
  vector<int> x(m);
  for(j=0;j<m;j++){
    cin>>x[j];
    y+=x[j];
  }
  z=abs(y);
  w=z/m;
  if(z%m*2>m) w++;
  if(y<0) w*=-1;
  for(j=0;j<m;j++) t+=(x[j]-w)*(x[j]-w);
  cout<<t<<endl;
}
### Prompt

Generate 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(){
  int m,j,y=0,z,w,t=0;
  cin>>m;
  vector<int> x(m);
  for(j=0;j<m;j++){
    cin>>x[j];
    y+=x[j];
  }
  z=abs(y);
  w=z/m;
  if(z%m*2>m) w++;
  if(y<0) w*=-1;
  for(j=0;j<m;j++) t+=(x[j]-w)*(x[j]-w);
  cout<<t<<endl;
}
```