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<bits/stdc++.h>
using namespace std;
int main(){
int N;
  cin>>N;
  vector<int>A(N);
  for(int i=0;i<N;i++)
    cin>>A.at(i);
  int sum=0;
  for(int i=0;i<N;i++)
    sum+=A.at(i);
  int x;
  if(sum%N<=N/2)
    x=sum/N;
  else
    x=(sum/N)+1;
  int ans=0;
  for(int i=0;i<N;i++)
    ans+=pow(x-A.at(i),2);
  cout<<ans<<endl;
   return 0;
}