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.io.PrintStream;
import java.util.TreeSet;
import java.io.InputStream;

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

    static class DArmchairs {
        int N;

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int i, j, k;

            N = in.nextInt();
            int[] A = in.getIntArray(N);

            TreeSet<Integer> avail = new TreeSet<>(), filled = new TreeSet<>();
            for (i = 0; i < N; ++i) if (A[i] == 1) filled.add(i + 1);
            for (i = 1; i <= N; ++i) if (!filled.contains(i)) avail.add(i);

            TreeSet<Integer> nextPass = new TreeSet<>();
            long ans = 0;
            for (int person : filled.descendingSet()) {
                Integer left = avail.floor(person), right = avail.ceiling(person);

                if (isValid(left) && isValid(right)) {
                    if (person - left <= right - person) {
                        avail.remove(left);
                        ans += person - left;
                    } else {
                        //avail.remove(right);
                        //ans += right - person;
                        nextPass.add(person);
                    }
                } else if (isValid(left)) {
                    avail.remove(left);
                    ans += person - left;
                } else {
                    //avail.remove(right);
                    //ans += right - person;
                    nextPass.add(person);
                }
            }

            // 0 .(x + 1)..1...(x)...0...(y)....1
            // x + 1 + y; x + y + 2x = y + 3x

            //System.err.println(nextPass);
            for (int person : nextPass.descendingSet()) {
                Integer left = avail.floor(person), right = avail.ceiling(person);

                if (isValid(left) && isValid(right)) {
                    if (person - left <= right - person) {
                        avail.remove(left);
                        ans += person - left;
                    } else {
                        avail.remove(right);
                        ans += right - person;
                    }
                } else if (isValid(left)) {
                    avail.remove(left);
                    ans += person - left;
                } else {
                    avail.remove(right);
                    ans += right - person;
                }
            }

            out.println(ans);
        }

        boolean isValid(Integer idx) {
            return idx != null && idx > 0 && idx <= N;
        }

    }

    static class FastReader {
        static final int BUFSIZE = 1 << 20;
        static byte[] buf;
        static int index;
        static int total;
        static InputStream in;

        public FastReader(InputStream is) {
            try {
                in = is;
                buf = new byte[BUFSIZE];
            } catch (Exception e) {
            }
        }

        private int scan() {
            try {
                if (index >= total) {
                    index = 0;
                    total = in.read(buf);
                    if (total <= 0)
                        return -1;
                }
                return buf[index++];
            } catch (Exception | Error e) {
                System.err.println(e.getMessage());
                return 13 / 0;
            }
        }

        public int nextInt() {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+')
                c = scan();
            for (; c >= '0' && c <= '9'; c = scan())
                val = (val << 3) + (val << 1) + (c & 15);
            return neg ? -val : val;
        }

        public int[] getIntArray(int size) {
            int[] ar = new int[size];
            for (int i = 0; i < size; ++i) ar[i] = nextInt();
            return ar;
        }

    }
}

