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

public class Education109 {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD(in, out);
        solver.solve();
        out.close();
    }

    static class TaskD {
        private final InputReader in;
        private final PrintWriter out;

        public TaskD(InputReader in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        public void solve() {
            int n = in.nextInt();
            int[] a = new int[n];

            for (int i = 0; i < n; ++i) {
                a[i] = in.nextInt();
            }

            Node currNode = new Node(0, 0, a[0]);
            Node firstNode = currNode;
            for (int i = 1; i < n; ++i) {
                if (a[i] == a[i - 1]) {
                    currNode.end++;
                } else {
                    Node newNode = new Node(i, i, a[i]);
                    currNode.next = newNode;
                    newNode.prev = currNode;

                    currNode = currNode.next;
                }
            }

            int sum = 0;
            currNode = firstNode;
            for (int i = 0; i < n; ++i) {
                if (i > currNode.end) {
                    currNode = currNode.next;
                }

                if (a[i] == 0) {
                    continue;
                }

                if (currNode.prev != null && (i - currNode.start <= currNode.end - i || currNode.next == null)) {
                    sum += i - currNode.start + 1;

                    Node prevNode = currNode.prev;
                    if (prevNode.getLen() != 1) {
                        prevNode.end--;
                        currNode.start--;
                    } else {
                        if (prevNode.prev != null) {
                            currNode.prev = prevNode.prev.prev;
                            currNode.start = prevNode.prev.start;
                        } else {
                            currNode.prev = null;
                            currNode.start--;
                        }
                    }
                } else {
                    sum += currNode.end - i + 1;

                    Node nextNode = currNode.next;
                    if (nextNode.getLen() != 1) {
                        nextNode.start++;
                        currNode.end++;
                    } else {
                        if (nextNode.next != null) {
                            currNode.next = nextNode.next.next;
                            currNode.end = nextNode.next.end;
                        } else {
                            currNode.next = null;
                            currNode.end++;
                        }
                    }
                }
            }

            out.println(sum);
        }
    }

    static class Node {
        Node next;
        Node prev;
        int start;
        int end;
        int value;

        public Node(int start, int end, int value) {
            this.start = start;
            this.end = end;
            this.value = value;
        }

        public int getLen() {
            return end - start + 1;
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public 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 nextInt() {
            return Integer.parseInt(next());
        }
    }
}
