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 main()
{
    int n,m=1e32,s,p,j,i,a[500];
    cin>>n;
    for(i=0;i<n;i++)cin>>a[i];
    sort(a,a+n);
    for(i=a[0];i<=a[n-1];i++)
    {
        s=0;
        for(j=0;j<n;j++)
        {
            p=(a[j]-i);
            s+=(p*p);
        }
        if(s<m)m=s;
    }
    cout<<m<<endl;
    return 0;
}