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,i,j=0,sm1=0,sm2=0,k;
 
 cin>>n;
 int a[n];
 for(i=0;i<n;i++)
 {
     cin>>a[i];
     j+=a[i];
 }
 k=j/n;
 j=ceil(j/(float)n);
 for(i=0;i<n;i++)
 {
     sm1+=(j-a[i])*(j-a[i]);
     sm2+=(k-a[i])*(k-a[i]);
 }
 cout<<min(sm1,sm2);
}