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.util.*;
import java.io.*;

public class D {
	private static BufferedReader br;
	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));

		solve();

		br.close();
	}

	private static void solve() throws IOException {
		int n = Integer.parseInt(br.readLine());
		boolean[] full = new boolean[n];
		int[] dist = new int[n];

		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i = 0; i < n; i++) {
			full[i] = Integer.parseInt(st.nextToken()) == 1;
		}

		boolean[] ogfull = full.clone();

		for (int i = 0; i < n; i++) {
			if (!ogfull[i]) {
				continue;
			}

			int r = 1;
			while ((i - r >= 0 || i + r < n) && ((i - r < 0 || (full[i - r] || ogfull[i - r])) && (i + r >= n || (full[i + r] || ogfull[i + r])))) {
				r++;
			}

			dist[i] = r;
			if (i - r >= 0 && !full[i - r] && !ogfull[i - r]) {
				full[i - r] = true;
			} else {
				full[i + r] = true;
			}
		}

		long ans = 0;
		for (int x : dist) {
			ans += x;
		}

		System.out.println(ans);
	}
}
