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 Solution
{
    
    static PrintWriter out = new PrintWriter(System.out);
    static FastReader in = new FastReader();
    static long mod = (long) 1e9 + 7;
      static List<List<Integer>> adj;
	public static void main (String[] args) throws java.lang.Exception
	{

	//	Scanner scan =new Scanner(System.in);
	
                   int n=in.nextInt();
                   int pos1=0;
                   int posn=0;
                   int[]  arr =  new int[n];
                    boolean[]  pre =  new boolean[n];
                    Arrays.fill(pre,false);
                   for(int i=0;i<n;i++){
                       arr[i]=in.nextInt();
                     if(arr[i]==1){
                         pre[i]=true;
                     }
                   }
                   int ans=0;
                   for(int i=0;i<n;i++){
                       if(arr[i]==1){
                           int left=i;
                           while(left>=0){
                               if(arr[left]==0){
                                   break;
                               }
                               left--;
                           }
                        int right=i;
                           while(right<n){
                               if(arr[right]==0){
                                   break;
                               }
                               right++;
                           }
                           if(left>0&&i-left<=right-i&&left!=i){
                               arr[left]=2;
                               arr[i]=-1;
                               ans+=i-left;
                           }else {
                                arr[right]=2;
                               arr[i]=-1;
                               ans+=right-i;
                           }
                            // System.out.println(i+" "+left+" "+right);  
                           
                       }
                   }
                  
                 System.out.println(ans);
                
                
 }
         static int GCD(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return GCD(b, a % b);
        }
    }

}

class FastReader {

    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }


}
