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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Iterator;
import java.util.Scanner;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author valeesi
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DArmchairs solver = new DArmchairs();
        solver.solve(1, in, out);
        out.close();
    }

    static class DArmchairs {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] arr = in.nextIntArray(n);
            TreeSet<Integer> busy = new TreeSet<>();
            TreeSet<Integer> free = new TreeSet<>();
            TreeSet<Integer> free2 = new TreeSet<>();
            TreeSet<Integer> free3 = new TreeSet<>();
            TreeSet<Integer> free4 = new TreeSet<>();
            int counter = 0;
            for (int i = 0; i < n; i++) {
                if (arr[i] != 1) {
                    free.add(i);
                    free2.add(i);
                    free3.add(i);
                    free4.add(i);
                } else {
                    busy.add(i);
                    counter++;
                }
            }

            if (counter == 0) {
                out.println(0);
                return;
            }

            int result = 0;

            for (Integer b : busy) {
                Integer lower = free.lower(b);
                Integer higher = free.higher(b);
                int lowerDiff = 0;
                int higherDiff = 0;

                if (lower != null) {
                    lowerDiff = Math.abs(lower - b);
                } else {
                    lowerDiff = Integer.MAX_VALUE;
                }

                if (higher != null) {
                    higherDiff = Math.abs(higher - b);
                } else {
                    higherDiff = Integer.MAX_VALUE;
                }

                if (lowerDiff > higherDiff) {
                    result += higherDiff;
                    free.remove(higher);
                } else if (lowerDiff < higherDiff) {
                    result += lowerDiff;
                    free.remove(lower);
                } else {
                    result += lowerDiff;
                    free.remove(lower);
                }
            }
            int result_temp = result;
            result = 0;
            for (Integer b : busy) {
                Integer lower = free3.lower(b);
                Integer higher = free3.higher(b);
                int lowerDiff = 0;
                int higherDiff = 0;

                if (lower != null) {
                    lowerDiff = Math.abs(lower - b);
                } else {
                    lowerDiff = Integer.MAX_VALUE;
                }

                if (higher != null) {
                    higherDiff = Math.abs(higher - b);
                } else {
                    higherDiff = Integer.MAX_VALUE;
                }

                if (lowerDiff > higherDiff) {
                    result += higherDiff;
                    free3.remove(higher);
                } else if (lowerDiff < higherDiff) {
                    result += lowerDiff;
                    free3.remove(lower);
                } else {
                    result += higherDiff;
                    free3.remove(higher);
                }
            }

            result_temp = Math.min(result, result_temp);
            result = 0;

            Iterator<Integer>
                    iterator = busy.descendingIterator();
            while (iterator.hasNext()) {
                Integer b = iterator.next();
                Integer lower = free2.lower(b);
                Integer higher = free2.higher(b);
                int lowerDiff = 0;
                int higherDiff = 0;

                if (lower != null) {
                    lowerDiff = Math.abs(lower - b);
                } else {
                    lowerDiff = Integer.MAX_VALUE;
                }

                if (higher != null) {
                    higherDiff = Math.abs(higher - b);
                } else {
                    higherDiff = Integer.MAX_VALUE;
                }

                if (lowerDiff > higherDiff) {
                    result += higherDiff;
                    free2.remove(higher);
                } else if (lowerDiff < higherDiff) {
                    result += lowerDiff;
                    free2.remove(lower);
                } else {
                    result += higherDiff;
                    free2.remove(higher);
                }
            }

            result_temp = Math.min(result, result_temp);
            result = 0;

            Iterator<Integer>
                    iterator2 = busy.descendingIterator();
            while (iterator2.hasNext()) {
                Integer b = iterator2.next();
                Integer lower = free4.lower(b);
                Integer higher = free4.higher(b);
                int lowerDiff = 0;
                int higherDiff = 0;

                if (lower != null) {
                    lowerDiff = Math.abs(lower - b);
                } else {
                    lowerDiff = Integer.MAX_VALUE;
                }

                if (higher != null) {
                    higherDiff = Math.abs(higher - b);
                } else {
                    higherDiff = Integer.MAX_VALUE;
                }

                if (lowerDiff > higherDiff) {
                    result += higherDiff;
                    free4.remove(higher);
                } else if (lowerDiff < higherDiff) {
                    result += lowerDiff;
                    free4.remove(lower);
                } else {
                    result += lowerDiff;
                    free4.remove(lower);
                }
            }

            out.println(Math.min(result_temp, result));
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public Scanner scanner;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            scanner = new Scanner(reader);
            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 nextInt() {
            return Integer.parseInt(next());
        }

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

    }
}

