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.

/**
* @author: Prasad Chaudhari
* @linkedIn: https://www.linkedin.com/in/prasad-chaudhari-841655a6/
* @git: https://github.com/Prasad-Chaudhari
*/
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;

public class Main {

    public static void main(String[] args) throws Exception {
        FastIO in = new FastIO(args);
        // int t = in.ni();
        int t = 1;
        while (t-- > 0) {
            int n = in.ni();
            int a[] = in.gia(n);
            boolean prefilled[] = new boolean[n];
            boolean currfilled[] = new boolean[n];
            for (int i = 0; i < n; i++)
                prefilled[i] = a[i] == 1;
            long ans = 0;
            for (int i = 0; i < n; i++) {
                boolean p = false;
                if (prefilled[i]) {
                    for (int j = i - 1; j >= 0; j--) {
                        if (!prefilled[j] && !currfilled[j]) {
                            currfilled[j] = true;
                            p = true;
                            ans += i - j;
                            // System.out.println(i + " " + j);
                            break;
                        }
                    }
                    if (!p) {
                        for (int j = i + 1; j < n; j++) {
                            if (!prefilled[j] && !currfilled[j]) {
                                currfilled[j] = true;
                                p = true;
                                ans += j - i;
                                // System.out.println(i + " " + j);
                                break;
                            }
                        }
                    }
                }
            }
            System.out.println(ans);
        }
        in.bw.flush();
    }

    static class Data implements Comparable<Data> {

        int a, b;

        public Data(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Data o) {
            if (a == o.a) {
                return Integer.compare(b, o.b);
            }
            return Integer.compare(a, o.a);
        }

        public static void sort(int a[]) {
            Data d[] = new Data[a.length];
            for (int i = 0; i < a.length; i++) {
                d[i] = new Data(a[i], 0);
            }
            Arrays.sort(d);
            for (int i = 0; i < a.length; i++) {
                a[i] = d[i].a;
            }
        }
    }

    static class FastIO {

        private final BufferedReader br;
        private final BufferedWriter bw;
        private String s[];
        private int index;

        public FastIO(String[] args) throws IOException {
            if (args.length > 1) {
                br = new BufferedReader(new InputStreamReader(new FileInputStream(new File(args[0]))));
                bw = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(new File(args[1]))));
            } else {
                br = new BufferedReader(new InputStreamReader(System.in));
                bw = new BufferedWriter(new OutputStreamWriter(System.out, "UTF-8"));
            }
            s = br.readLine().split(" ");
            index = 0;
        }

        public int ni() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public double nd() throws IOException {
            return Double.parseDouble(nextToken());
        }

        public long nl() throws IOException {
            return Long.parseLong(nextToken());
        }

        public String next() throws IOException {
            return nextToken();
        }

        public String nli() throws IOException {
            try {
                return br.readLine();
            } catch (IOException ex) {

            }
            return null;
        }

        public int[] gia(int n) throws IOException {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[] gia(int n, int start, int end) throws IOException {
            validate(n, start, end);
            int a[] = new int[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public double[] gda(int n) throws IOException {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }

        public double[] gda(int n, int start, int end) throws IOException {
            validate(n, start, end);
            double a[] = new double[n];
            for (int i = start; i < end; i++) {
                a[i] = nd();
            }
            return a;
        }

        public long[] gla(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }

        public long[] gla(int n, int start, int end) throws IOException {
            validate(n, start, end);
            long a[] = new long[n];
            for (int i = start; i < end; i++) {
                a[i] = nl();
            }
            return a;
        }

        public void print(String s) throws IOException {
            bw.write(s);
        }

        public void println(String s) throws IOException {
            bw.write(s);
            bw.newLine();
        }

        public void print(int s) throws IOException {
            bw.write(s + "");
        }

        public void println(int s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        public void print(long s) throws IOException {
            bw.write(s + "");
        }

        public void println(long s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        public void print(double s) throws IOException {
            bw.write(s + "");
        }

        public void println(double s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        private String nextToken() throws IndexOutOfBoundsException, IOException {
            if (index == s.length) {
                s = br.readLine().split(" ");
                index = 0;
            }
            return s[index++];
        }

        private void validate(int n, int start, int end) {
            if (start < 0 || end >= n) {
                throw new IllegalArgumentException();
            }
        }
    }
}
