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, ans = 1e9;
  scanf("%d", &n);
  int a[n];
  for(i = 0; i < n; ++i) scanf("%d", &a[i]);
  for(i = -100; i <= 100; ++i) {
    int now = 0;
    for(j = 0; j < n; ++j) now += (i - a[j]) * (i - a[j]);
    if(now < ans) ans = now;
  }
  printf("%d", ans);
  return 0;
}