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 sol{
    public static void main(String args[])throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine().trim());
        int arr[] = new int[n];
        String a[] = br.readLine().split(" ");
        for(int i=0 ;i<n ; i++){
            arr[i] = Integer.parseInt(a[i]);
        }
        long ans = 0;
        int marked[] = new int[n];
        for(int i=0 ; i<n ; i++){
            if(arr[i] == 1){
                marked[i]=1;
            }
        }
        for(int i=0 ; i<n ; i++){
            if(arr[i] == 1){
                int temp = Integer.MAX_VALUE;
                int cur = 0;
                for(int j=0 ; j<n ; j++){
                    if(i!=j){
                        int res = Math.abs(j-i);
                        if(res != 1 && res < temp && marked[j] == 0){
                            temp = res;
                            cur = j;
                        }if(res == 1 && marked[j] == 0){
                            temp = 1;
                            cur = j;
                            break;
                        }
                    }
                }
                ans += (long)temp;
                marked[cur] = 1;
            }
        }
        System.out.println(ans);
    }
}