#include<bits/stdc++.h>
using namespace std;
 
int main(){
  int n, a, x = 0, y = 0;
  scanf("%d", &n);
  for(int i = 0; i < n; i++){
    scanf("%d", &a);
    x += a*a;
    y += a;
  }
  printf("%d\n", x + (n*(y/n + (y%n > n/2)) - 2*y)*(y/n + (y%n > n/2)));
}

### Prompt

In Cpp, your task is to solve 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 n, a, x = 0, y = 0;
  scanf("%d", &n);
  for(int i = 0; i < n; i++){
    scanf("%d", &a);
    x += a*a;
    y += a;
  }
  printf("%d\n", x + (n*(y/n + (y%n > n/2)) - 2*y)*(y/n + (y%n > n/2)));
}

```