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 ques4 {
    static 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;
        }
    }

    public static void main(String[] args) throws NumberFormatException, IOException {
        FastReader scn = new FastReader();
        // long t = scn.nextInt();
        // for (int i = 0; i < t; i++) {
            int n=scn.nextInt();
            int[] arr=new int[n];
            ArrayList<Integer> i1=new ArrayList<>();
            ArrayList<Integer> i0=new ArrayList<>();
            int count=0;
            for(int j=0;j<n;j++){
                arr[j]=scn.nextInt();
                if(arr[j]==1){
                    i1.add(j);
                }
                else{
                    i0.add(j);
                }
            }
            int start=1;
            // int end=n-1;
            int minIndex0=0;
            int minIndex1=0;
            int ans=0;
            while(!i1.isEmpty()){
                int minS=Math.abs(i1.get(0)-i0.get(0));
                if(i0.size()==1){
                    ans+=Math.abs(i1.get(0)-i0.get(0));
                    break;
                }
                
                start=1;
                while(start<i0.size()&&Math.abs(i1.get(0)-i0.get(start))<minS){
                    minS=Math.abs(i1.get(0)-i0.get(start));
                    start++;
                }
                // System.out.println(minS);
                ans+=minS;
                i1.remove(0);
                i0.remove(start-1);
                if(i1.size()>1){
                int end=i0.size()-2;
                minS=Math.abs(i1.get(i1.size()-1)-i0.get(i0.size()-1));

                while(end>=0&&Math.abs(i1.get(i1.size()-1)-i0.get(end))<minS){
                    minS=Math.abs(i1.get(i1.size()-1)-i0.get(end));
                    end--;
                    // System.out.println("done");System.out.println(minS);
                }
                ans+=minS;
                
                i1.remove(i1.size()-1);
                i0.remove(end+1);}
            }
            System.out.println(ans);
        }
    }
// }
