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(void)
{
	int i,j,n,x=-1000,y=1000000,z[100],a,b,c=0,d=2100000000;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		scanf("%d",&z[i]);
		if(x<z[i]){
			x=z[i];
		}
		if(y>z[i]){
			y=z[i];
		}
	}
	for(i=y;i<=x;i++){
		c=0;
		for(j=1;j<=n;j++){
			c+=(i-z[j])*(i-z[j]);
		}
		if(d>c){
			d=c;
		}
	}
	printf("%d\n",d);
	return 0;
}