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.InputStreamReader;
import java.util.*;

public class Main {

    public static long gdc(long a, long b) {
        if (b > a) {
            long t = a;
            a = b;
            b = t;
        }

        while (a % b != 0) {
            long t = a % b;
            a = b;
            b = t;
        }
        return b;
    }

    public static void test() {
        int n = 6;
        Random r = new Random();
        int t = 1000;
        while (t-- > 0) {
            int ones = r.nextInt(n / 2) + 1;

            int v[] = new int[n];

            for (int i = 0; i < n; i++) {
                if (ones > 0) {
                    v[i] = r.nextInt(2);
                    if (v[i] == 1) {
                        ones--;
                    }
                } else {
                    v[i] = 0;
                }
            }
            int smart = cc(n, v);
            int greedy = c(n, v);

            if (smart != greedy) {
                System.out.println(smart + " " + greedy + " " + Arrays.toString(v));
                break;
            }
        }

        System.out.println("done!");
    }

    public static void main(String[] args) throws IOException {

//        test();

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 1024 * 1024 * 2);

//        int t = Integer.parseInt(br.readLine());
        StringBuilder sb = new StringBuilder();

//        while (t-- > 0) {
        int n = Integer.parseInt(br.readLine());
        int[] v = readArrayLine(br.readLine(), n);
        sb.append(cc(n, v)).append('\n');
//        }

        System.out.println(sb.toString());
    }

    private static int cc(int n, int[] v) {
        List<Integer> ones = new ArrayList<>();
        List<Integer> zeros = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            if (v[i] == 1) {
                ones.add(i);
            } else {
                zeros.add(i);
            }
        }

        if (ones.size() == 0) {
            return 0;
        }

        int[][] d = new int[ones.size()][zeros.size()];
        for (int i = 0; i < ones.size(); i++) {
            if (i == 0) {
                for (int j = 0; j < zeros.size(); j++) {
                    d[i][j] = Math.abs(ones.get(i) - zeros.get(j));
                }
            } else {
                int minCost = Integer.MAX_VALUE;
                for (int j = 0; j < i; j++) {
                    minCost = Math.min(d[i - 1][j], minCost);
                    d[i][j] = Integer.MAX_VALUE;
                }
                for (int j = i; j < zeros.size(); j++) {
                    d[i][j] = Math.abs(ones.get(i) - zeros.get(j)) + minCost;
                    minCost = Math.min(d[i - 1][j], minCost);
                }
            }
        }

        int min = Integer.MAX_VALUE;
        for (int j = 0; j < zeros.size(); j++) {
            min = Integer.min(min, d[ones.size() - 1][j]);
        }

        return min;
    }

    private static int c(int n, int[] v) {

        LinkedList<Integer> zeros = new LinkedList<>();
        for (int i = 0; i < n; i++) {
            if (v[i] == 0) {
                zeros.add(i);
            }
        }

        int ones = n - zeros.size();
        int cost = 0;
        for (int i = 0; i < n; i++) {
            if (v[i] == 1) {
                if (ones == zeros.size()) {
                    int j = zeros.poll();
                    ones--;
                    cost += Math.abs(j - i);
                } else {
                    int min = Integer.MAX_VALUE;
                    int jj = -1;
                    for (int j : zeros) {
                        int dist = Math.abs(j - i);
                        if (dist < min) {
                            min = dist;
                            jj = j;
                        }
                    }
                    zeros.remove((Integer) jj);
                    ones--;
                    cost += min;
                }
            }
        }

        return cost;
    }

    private static int b(int n, int[] v) {
        boolean sorted = true;
        for (int i = 1; i < n; i++) {
            if (v[i] < v[i - 1]) {
                sorted = false;
                break;
            }
        }
        int count = 0;
        if (!sorted) {
            if (v[0] == 1 || v[n - 1] == n) {
                count = 1;
            } else if (v[0] == n && v[n - 1] == 1) {
                count = 3;
            } else {
                count = 2;
            }
        }

        return count;
    }

    private static long solve() {
        return 0;
    }

    public static int[] readArrayLine(String line, int n) {
        return readArrayLine(line, n, null, 0);
    }

    private static int[] readArrayLine(String line, int n, int array[], int pos) {
        int[] ret = array == null ? new int[n] : array;
        int start = 0;
        int end = line.indexOf(' ', start);
        for (int i = pos; i < pos + n; i++) {
            if (end > 0)
                ret[i] = Integer.parseInt(line.substring(start, end));
            else
                ret[i] = Integer.parseInt(line.substring(start));
            start = end + 1;
            end = line.indexOf(' ', start);
        }
        return ret;
    }
}
