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.
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    /*static long power(long a,long b,long m)
    {
        if(b==0)
        return 1;
        if((b&1)==0)
        return power((a*a)%m,b/2,m);
        else
        return (a*power((a*a)%m,b/2,m))%m;
    }*/
    /*
    static int gcd(int a,int b)
    {
        if(b==0)
        return a;
        else
        return gcd(b,a%b);
    }
    */
    public static void main (String[] args) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter p=new PrintWriter(System.out);
            //StringTokenizer st=new StringTokenizer(br.readLine());
            int n=Integer.parseInt(br.readLine());
            int a[]=new int[n];
            StringTokenizer st=new StringTokenizer(br.readLine());
            for (int i=0;i<n ;i++)
            a[i]=Integer.parseInt(st.nextToken());
            List<Integer> emp=new ArrayList<>();
            for(int i=0;i<n;i++)
            if(a[i]==0)
            emp.add(i);
            if(emp.size()==n)
            {
                p.println("0");
                p.flush();
                System.exit(0);
            }
            if(emp.size()==n-1)
            {
                p.println("1");
                p.flush();
                System.exit(0);
            }
            int c=0;
            for(int i=0;i<n;i++)
            {
                if(a[i]==1)
                {
                    int m=4999,mi=0;
                    for(int j=0;j<emp.size();j++)
                    {
                        if(Math.abs(emp.get(j)-i)<m)
                        {
                            m=Math.abs(emp.get(j)-i);
                            mi=j;
                        }
                    }
                    c+=m;
                    emp.remove(mi);
                }
            }
            p.println(c);
            p.flush();
        
	}
}
