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>
#define ll long long

using namespace std;

int main(){
  ll N,m=1e9;
  cin>>N;
  ll a[N];
  for(ll i=0;i<N;i++) cin>>a[i];
  sort(a,a+N);
 
  for(ll i=a[0];i<=a[N-1];i++){
    ll x=0;
    for(ll j=0;j<N;j++){
      ll y=(i-a[j])*(i-a[j]);
      x+=y;
    }
    m=min(m,x);
  }
  cout<<m<<endl;
}
