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 Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
		int n=Integer.parseInt(br.readLine());
	    String s[]=br.readLine().split(" ");
	    int arr[]=new int[n];
	    HashSet<Integer> hs=new HashSet<>();
	    HashSet<Integer> hs1=new HashSet<>();
	    for(int i=0;i<n;i++) {
	    	arr[i]=Integer.parseInt(s[i]);
	    	if(arr[i]!=1) {
	    		hs.add(i+1);
	    	}else {
	    		hs1.add(i+1);
	    	}	
	    }
	    int ans=0;
	    for(int i=1;i<n;i+=2) {
	    	HashSet<Integer> t1=new HashSet<>();
	    	for(int h1:hs1) {
	    		if(h1-i>0&&hs.contains(h1-i)) {
	    			ans+=i;
	    			hs.remove(h1-i);
	    			continue;
	    		}
	    		if(h1+i<=n&&hs.contains(h1+i)) {
	    			ans+=i;
	    			hs.remove(h1+i);
	    			continue;
	    		}
	    		t1.add(h1);
	    	}
	    	hs1=t1;
	    }
	    bw.write(ans+"\n");
		bw.flush();
	}
}
