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>
using namespace std;
int v[1000],n,s,a,b,c,i;
int main()
{
	cin>>n;
    for(i=1;i<=n;i++)
    {
    cin>>v[i];
    s+=v[i];
	}
	s/=n;
	for(i=1;i<=n;i++)
	{
		a+=(v[i]-s+1)*(v[i]-s+1);
		b+=(v[i]-s)*(v[i]-s);
		c+=(v[i]-s-1)*(v[i]-s-1);
	}
	cout<<min(min(a,b),c);
}