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 armchairs {

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

		int n = Integer.parseInt(br.readLine());
		String[] st = br.readLine().split(" ");

		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = Integer.parseInt(st[i]);
		}

		boolean[] vis = new boolean[n];
		long time = 0;
		int zerocount = 0;

		for (int i = 0; i < n; i++) {
			if (arr[i] == 0) {
				if (vis[i] == false) {
					zerocount++;
				}
				continue;
			}

			if (zerocount > 0) {
				int count = 1;
				while (true) {
					int back = i - count;
					if (back >= 0 && arr[back] == 0 && vis[back] == false) {
						time += (i - back);
						vis[back] = true;
						zerocount--;
						break;
					}
					count++;
				}
			} else {
				int count = 1;
				while (true) {
					int front = i + count;
					if (front < n && arr[front] == 0 && vis[front] == false) {
						time += (front - i);
						vis[front] = true;
						break;
					}
					count++;
				}
			}
		}

		System.out.println(time);
	}
}
