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>
#include<cmath>
using namespace std;

int main(){
	int N,ans=0,minv=(1<<20);
  	cin>>N;
  	vector<int>a(N);
	for(int i=0;i<N;++i)cin>>a[i];
  	for(int i=-100;i<=100;++i){
      	ans=0;
    	for(int j=0;j<N;++j){
        	ans+=pow((i-a[j]),2);
		 }minv=min(minv,ans);
    }cout<<minv<<endl;
  	return 0;
}