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.*;
import java.io.*;
public class armchairs
{
    static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    public static void main(String[] args)throws IOException
    {
        int n=Integer.parseInt(in.readLine());
        String s=in.readLine();
        String[] st = s.trim().split("\\s+");
        int a[]=new int[n];int n1=0;boolean ch=true;
        for(int i=0;i<n;i++)
        {
            a[i]=Integer.parseInt(st[i]);
            if(a[i]==1)
            n1++;
        }
        int co=0,j=0;
        for(int i=0;i<n;i++)
        {
            if(n1>0)
            {
            if(a[i]==0&&a[i+1]==1)
            {
                co+=1;
                a[i]=2;
                a[i+1]=2;
                n1--;
                continue;
            }
              
            if(a[i]==1)
            {
                j=i+1;
                if(i==n-1){
                    ch=false;
                    j=i-1;
                }
                while(a[j]!=0) {
                    if(j+1==n)
                    ch=false;
                    if(ch)
                    j++;
                    else
                    j--;
                }
                co+=Math.abs(j-i);
                a[j]=2;
            }
            else
            continue;
            n1--;
        }
        }
        System.out.println(co);
        }
    }