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 Main
{
	public static void main(String[] args)
	{
		Scanner sc=new Scanner(System.in);
		    int n=sc.nextInt();
		    int arr[]=new int[n];
		    ArrayList<Integer> list1=new ArrayList<>();
		    ArrayList<Integer> list2=new ArrayList<>();
		    for(int i=0;i<n;i++)
		    {
		        arr[i]=sc.nextInt();
		        if(arr[i]==1)
		        list1.add(i);
		    }
		    int ans=0;
		    for(int i=0;i<list1.size();i++)
		    {
		        int num=list1.get(i);
		        int j=1;
		        while(num-j>=0 || num+j<n)
		        {
		            int x1=num-j>=0?arr[num-j]:-1;
		            int x2=num+j<n?arr[num+j]:-1;
		            if(x1==0 && !list2.contains(num-j))
		            {
		                list2.add(num-j);
		                break;
		            }
		            if(x2==0 && !list2.contains(num+j))
		            {
		                list2.add(num+j);
		                break;
		            }
		            j++;
		        }
		        ans+=j;
		    }
		    System.out.println(ans);
	}
}
