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 Arm_chair {
    public static void main (String args[]) throws Exception
    {
        Scanner Sc= new Scanner (System.in);
        int n=Sc.nextInt();
        //int x=n;
        int [] arr= new int [n];
        int [] pos=new int [n];
        int w=0;
        for(int a=0;a<n;a++)
        {
          arr[a]=Sc.nextInt();
          if (arr[a]==1)
          {
              pos[w]=a;
              w++;
          }
        }
        
        int counter =0;
        int f =1;
        for(int j=0;j<n;j++)
        {
            if(pos[j]==0&&pos[j+1]==0)
            {   if(pos[0]==0&&pos[1]==0)
                {
                    counter =-1;
                } 
                break;
            }
            
            if(pos[j+1]-pos[j]==1)
            {
                f++;
            }
            if(pos[j+1]-pos[j]>1)
            {
                counter ++;
            }
            
        }
        if(f == 2)
        counter =counter +3;
        else
        {
        counter = counter +f*f ;
        }
        System.out.println(counter);
        Sc.close();
    }
}
   

