There are n armchairs, numbered from 1 to n from left to right. Some armchairs are occupied by people (at most one person per armchair), others are not. The number of occupied armchairs is not greater than n/2.

For some reason, you would like to tell people to move from their armchairs to some other ones. If the i-th armchair is occupied by someone and the j-th armchair is not, you can tell the person sitting in the i-th armchair to move to the j-th armchair. The time it takes a person to move from the i-th armchair to the j-th one is |i - j| minutes. You may perform this operation any number of times, but these operations must be done sequentially, i. e. you cannot tell a person to move until the person you asked to move in the last operation has finished moving to their destination armchair.

You want to achieve the following situation: every seat that was initially occupied must be free. What is the minimum time you need to do it?

Input

The first line contains one integer n (2 ≤ n ≤ 5000) — the number of armchairs.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 1). a_i = 1 means that the i-th armchair is initially occupied, a_i = 0 means that it is initially free. The number of occupied armchairs is at most n/2.

Output

Print one integer — the minimum number of minutes you have to spend to achieve the following situation: every seat that was initially occupied must be free.

Examples

Input


7
1 0 0 1 0 0 1


Output


3


Input


6
1 1 1 0 0 0


Output


9


Input


5
0 0 0 0 0


Output


0

Note

In the first test, you can perform the following sequence:

  1. ask a person to move from armchair 1 to armchair 2, it takes 1 minute; 
  2. ask a person to move from armchair 7 to armchair 6, it takes 1 minute; 
  3. ask a person to move from armchair 4 to armchair 5, it takes 1 minute. 



In the second test, you can perform the following sequence:

  1. ask a person to move from armchair 1 to armchair 4, it takes 3 minutes; 
  2. ask a person to move from armchair 2 to armchair 6, it takes 4 minutes; 
  3. ask a person to move from armchair 4 to armchair 5, it takes 1 minute; 
  4. ask a person to move from armchair 3 to armchair 4, it takes 1 minute. 



In the third test, no seat is occupied so your goal is achieved instantly.
import java.util.*;

public class D {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        ArrayList<Integer> vacant = new ArrayList<>();
        ArrayList<Integer> occupied = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int x = scanner.nextInt();
            if(x == 0)
                vacant.add(i);
            else
                occupied.add(i);
        }
        long res = 0;
        ArrayList<Integer> optimals = new ArrayList<>();
        ArrayList<Integer> persons = new ArrayList<>();
        while (!occupied.isEmpty()) {
            int person = occupied.remove(0);
            persons.add(person);
            int min = Integer.MAX_VALUE;
            int index = -1;
            for (int i = 0; i < vacant.size(); i++) {
                int difference = Math.abs(person - vacant.get(i));
                if(difference < min) {
                    min = difference;
                    index = i;
                }
            }
            res += min;
            optimals.add(vacant.remove(index));
        }
        Collections.sort(persons);
        Collections.sort(optimals);
        long ans = 0;
        for (int i = 0; i < persons.size(); i++) {
            ans += (Math.abs(persons.get(i) - optimals.get(i)));
        }
        System.out.println(Math.min(res, ans));
    }
}
