#include<cstdio>
#include<cmath>

int N, aver, sum = 0, result = 0;

int main() {
    scanf("%d", &N);
    int a[N];
    for(int i=0; i<N; i++) {
    	scanf("%d", &a[i]);
    	sum += a[i];
    }
    aver = round(1.0 * sum / N);
    for(int i=0; i<N; i++) {
    	result += pow(aver-a[i], 2);
    }
    printf("%d\n", result);
    return 0;
}
### Prompt

Please create a solution in Cpp 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<cstdio>
#include<cmath>

int N, aver, sum = 0, result = 0;

int main() {
    scanf("%d", &N);
    int a[N];
    for(int i=0; i<N; i++) {
    	scanf("%d", &a[i]);
    	sum += a[i];
    }
    aver = round(1.0 * sum / N);
    for(int i=0; i<N; i++) {
    	result += pow(aver-a[i], 2);
    }
    printf("%d\n", result);
    return 0;
}
```