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.*;

public class Solution {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		StringBuffer out=new StringBuffer();

		int t=1;

		while(t--!=0) {

			int n=in.nextInt();

			ArrayList<Integer> list[]=new ArrayList[2];
			for(int i=0; i<2; i++)
				list[i]=new ArrayList<>();

			for (int i=0; i<n; i++) {
				list[in.nextInt()].add(i);	
			}

			int x=list[0].size(),
				y=list[1].size();

			out.append(solve(x-1, y-1, list, new Integer[x][y]));
		}

		System.out.println(out);
	}

	private static int solve(int i, int j, ArrayList<Integer> list[], Integer dp[][]) {
		if(i<j)
			return Integer.MAX_VALUE;

		if(j<0)
			return 0;

		if(dp[i][j]!=null)
			return dp[i][j];

		return dp[i][j]=Math.min(Math.abs(list[0].get(i)-list[1].get(j))+solve(i-1, j-1, list, dp),
									solve(i-1, j, list, dp));
	}

	private static int GCD(int a, int b) {
		if(a==0)
			return b;
		return GCD(b%a, a);
	}
}