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()
{
	int n, resp = INT_MAX;
	cin >> n;
	vector<int> vec(n);
	for(auto &x: vec) cin >> x;
		
	for(int i = -100; i<= 100; i++)
	{
		int acc = 0;
		for(auto a: vec)
			acc += (a - i)*(a - i);
		resp = min(acc, resp);
	}
	cout << resp << '\n';
	return 0;
}