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,c=0,mi=INT_MAX;
   cin>>n;
   ll arr[n];
   for(int i=0;i<n;i++)
    cin>>arr[i];
   for(int i=-100;i<=100;i++){
       for(int o=0;o<n;o++){
        c=pow(abs(i-arr[o]),2)+c;
    }
    mi=min(c,mi);
    c=0;
   }
   cout<<mi;
   return 0;
}