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<stdio.h>
int main(){
int a=0;
int b[100];
int s=0;
int c=0;
int d=0;
int ss=0;
for(int i=0;i<100;i++){
b[i]=0;
}
scanf("%d",&a);
for(int i=0;i<a;i++){
scanf("%d",&b[i]);
s=s+b[i];

}

d=s%a;
c=s/a;

if(d>(a/2)){
c++;
}
for(int i=0;i<a;i++){
int j=b[i]-c;
ss=j*j+ss;
}
printf("%d",ss);
return 0;
}
