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;

public class _109D {
    static BufferedReader br;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        int n = readInt();
        int arr[] = readIntarray();
        int []a = new int[n];
        int []b = new int[n];
        for(int i = 0; i < n; i++){
            a[i] = arr[i];
        }
        int t_ans = 0;
        for(int i = 0; i < n; i++){
            if (arr[i] == 1) {
                for (int step = 1; step < n; step++) {
                    if ((i - step) >= 0 && a[i - step]==0 && b[i - step]==0) {
                        b[i-step] = 1;
                        t_ans += step;
                        step=n;
                    }else if((i + step)<n && a[i + step] == 0 && b[i + step]==0){
                        b[i+step] = 1;
                        t_ans += step;
                        step=n;
                    }
                }
            }
        }
        int ans = 0;
        for(int i = 0; i < n; i++){
            if (b[i] == 1) {
                boolean done = false;
                for (int step = 1; (!done) && step < n; step++) {
                    if ((i - step) >= 0 && a[i - step]==1) {
                        ans += step;
                        a[i-step] = 0;
                        step = n;
                        done = true;
                    }
                }
                for (int step = 1; (!done) && step < n; step++) {
                    if((i + step)<n && a[i + step]==1){
                        a[i+step] = 0;
                        ans += step;
                        step=n;
                        done = true;
                    }
                }
            }
        }
//        for(int i = 0; i< n; i++){
//            System.out.print(arr[i]+" ");
//        }
//        System.out.println();
//        for(int i = 0; i< n; i++){
//            System.out.print(b[i]+" ");
//        }
//        System.out.println();
//        System.out.println(Math.min(ans, t_ans));
        System.out.println(ans);
    }


    static int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    static long readLong() throws IOException {
        return Long.parseLong(br.readLine());
    }

    static int[] readIntarray() throws IOException {
        String[] _a = br.readLine().split(" ");
        int[] _res = new int[_a.length];
        for (int i = 0; i < _a.length; i++) {
            _res[i] = Integer.parseInt(_a[i]);
        }
        return _res;
    }

    static long[] readLongarray() throws IOException {
        String[] _a = br.readLine().split(" ");
        long[] _res = new long[_a.length];
        for (int i = 0; i < _a.length; i++) {
            _res[i] = Long.parseLong(_a[i]);
        }
        return _res;
    }
}
