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.*;
import java.math.*;

public class Main {
    static InputReader in;
    static OutputWriter out;


    static void solve(){
        int n= in.nextInt();
        int[] arr= in.nextIntArray(n);
        ArrayList<Integer> l1= new ArrayList<>();
        ArrayList<Integer> l2= new ArrayList<>();
        for(int i=0;i<n;i++){
            if(arr[i]==1) l1.add(i);
            else l2.add(i);
        }
        Collections.sort(l1);
        Collections.sort(l2);
        
        int total=0;  
        boolean[] visited= new boolean[n];
        for(int i=n-1;i>=0;i--){
            if(arr[i]==0) continue; 
            int min= Integer.MAX_VALUE;
            int ind=0;
            int c1=0;
            int c0=0;
            int flag=0;
            for(int j=0;j<i;j++){
                if(arr[j]==1) c1++;
            }
            for(int j=0;j<n;j++){
                if(arr[j]==0 && !visited[j]) c0++;
                if(c0>c1){
                    ind= j;
                    break;
                }
            }
            for(int j=ind;j<n;j++){
                if(visited[j]|| arr[j]==1) continue;
                if(Math.abs(i-j)<=min){
                    min= Math.abs(i-j);
                    ind=j;
                }
            }
            visited[i]=true;
            visited[ind]= true;
            total+= min;
        }
        out.println(total);

     }

  

    public static void main(String[] args) throws IOException{
       
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        if (System.getProperty("ONLINE_JUDGE") == null) {
            inputStream = new FileInputStream("input.txt");
            outputStream = new FileOutputStream("output.txt");
        } else {
            inputStream = System.in;
            outputStream = System.out;
        }
        in = new InputReader(inputStream);
        out = new OutputWriter(outputStream);

        int testCount = 1;
        // testCount= in.nextInt();
        for (int i = 1; i <= testCount; i++)
            solve();
        out.flush();out.close();

    }

    public static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
       
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int[] nextIntArray(int n){
            int[] array=new int[n];
            for(int i=0;i<n;++i)array[i]=nextInt();
            return array;
        }
        public long[] nextLongArray(int n){
            long[] array=new long[n];
            for(int i=0;i<n;++i)array[i]=nextLong();
            return array;
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public String nextLine() {
            String str = "";
            try {
                str = reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static class OutputWriter {
        private PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println() {
            writer.println();
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }
         public void close() {
            writer.close();
         }       

    public void flush() {
        writer.flush();
    }
    }
}   