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

int main(void){
	int N,sum=0;
	cin >> N;
	int a[N];
	for(int i=0;i<N;i++){
		cin >>a[i];
		sum += a[i];
	}
	if(sum%N> N/2){
		sum = (sum+(N-1))/N;
	}else{
		sum /=N;
	}
	long long ans = 0;
	for(int i=0;i<N;i++){
		ans += (sum-a[i])*(sum-a[i]);
	}
	cout << ans;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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,sum=0;
	cin >> N;
	int a[N];
	for(int i=0;i<N;i++){
		cin >>a[i];
		sum += a[i];
	}
	if(sum%N> N/2){
		sum = (sum+(N-1))/N;
	}else{
		sum /=N;
	}
	long long ans = 0;
	for(int i=0;i<N;i++){
		ans += (sum-a[i])*(sum-a[i]);
	}
	cout << ans;
}
```