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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main
{
	public static void main(String[] args)
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[] a=new int[n];
		for(int i=0;i<n;i++)
			a[i]=sc.nextInt();
		ArrayList<Integer> pos=new ArrayList<>(n);
		for(int i=0;i<n;i++)
			if(a[i]==1)
				pos.add(i);
		int k=pos.size();
		int[][] dp=new int[n+1][k+1];
		for(int i=0;i<n+1;i++)
			Arrays.fill(dp[i], Integer.MAX_VALUE);
		dp[0][0]=0;
		for(int i=0;i<n;i++)
			for(int j=0;j<=k;j++)
			{
				if(dp[i][j]==Integer.MAX_VALUE)
					continue;
				dp[i+1][j]=Math.min(dp[i+1][j], dp[i][j]);
				if(j<k && a[i]==0)
					dp[i+1][j+1]=Math.min(dp[i+1][j+1], dp[i][j]+Math.abs(pos.get(j)-i));
			}
		System.out.println(dp[n][k]);
    }
}