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>
#include <stdlib.h>
#include <math.h>

int a[105];

int main() {
  int N, M, ans = 0;
  double m, sum = 0;
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    scanf("%d", &a[i]);
    sum += a[i];
  }
  m = sum / N;
  M = round(m);
  for (int i = 0; i < N; i++) {
    ans += pow( abs(a[i] - M), 2) ;
  }
  printf("%d\n", ans);
}
