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

#include <iostream>
#include<vector>
using namespace std;

int main() {
	int n;cin>>n;
	vector<int> a(n);
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	int ans=-1;
	int anst;
	for(int m=-100;m<=100;m++){
		anst=0;
		for(auto x:a){
			anst+=(x-m)*(x-m);
		}
		if(ans>anst)ans=anst;
		if(ans==-1)ans=anst;
	}
	cout<<ans<<endl;
	return 0;
}
