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.*;
import java.util.*;
import java.util.StringTokenizer;


public class Main {
    public static void main(String[] args) throws IOException {
//        InputReader sc = new InputReader(System.in);
//        PrintWriter out = new PrintWriter(System.out);
        BufferedReader br = new BufferedReader(
                new InputStreamReader(System.in));

      FastReader reader =new FastReader();
        BufferedWriter output = new BufferedWriter(
                new OutputStreamWriter(System.out));
        int test = 1;
        for (int o = 0; o < test; o++){
            int n = reader.nextInt();
            int[] arr = new int[n];
            ArrayList<Integer> l1 = new ArrayList<>();
            ArrayList<Integer> l0 = new ArrayList<>();
            TreeSet<Integer> set= new TreeSet<>();
            for (int i = 0; i < n; i++){
                arr[i] = reader.nextInt();
                if (arr[i] == 1){l1.add(i);}
                else {
                    l0.add(i);
                    set.add(i);
                }
            }
       //   System.out.println(l1 + " " + l0);
            long ans = 0;
            int k = l1.size();
            for (int i = 0; i < k; i++){
                Integer s1 = set.lower(l1.get(i)) ;
                Integer s2 = set.higher(l1.get(i));
                if (s1 == null) s1= 100000000;
                if (s2 == null) s2 = 100000000;
                int k1 = Math.abs(s1 - l1.get(i));
                int k2 = Math.abs(s2 - l1.get(i));
                if (k1 <= k2){
                    ans += k1;
                    set.remove(s1);
                }
                else {
                    ans += k2;
                    set.remove(s2);
                }

            }

            System.out.println(ans);
        }
        }
        public static int gcd(int a, int b){
            if (a == 0)
                return b;
            if (b == 0)
                return a;

            // base case
            if (a == b)
                return a;

            // a is greater
            if (a > b)
                return gcd(a-b, b);
            return gcd(a, b-a);

        }
    }


class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}