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.
//package currentContest;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;
public class P4 {
	static int dp[][]=new int[5000+1][5000+1];
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader sc=new FastReader();
		int t=1;
		//t=sc.nextInt();
		StringBuilder s=new StringBuilder();
		while(t--!=0) {
			int n=sc.nextInt();
			int a[]=new int[n];
			
			for(int i=0;i<=n;i++) {
				for(int j=0;j<=n;j++) {
					P4.dp[i][j]=-1;
				}
			}
			ArrayList<Integer> one=new ArrayList<>();
			ArrayList<Integer> zero=new ArrayList<>();
			for(int i=0;i<n;i++) {
				a[i]=sc.nextInt();
				if(a[i]==0) {
					zero.add(i);
				}else {
					one.add(i);
				}
			}
			Collections.sort(zero);
			Collections.sort(one);
			long ans=sol(0,0,zero.size(),one.size(),a,zero,one);
			System.out.println(ans);
		}
		//System.out.println(s);
	}
	private static long sol(int i, int j, int n, int m,int a[], ArrayList<Integer> zero, ArrayList<Integer> one) {
		//System.out.println(i+" "+j);
		// TODO Auto-generated method stub
		if(j==m) {
			return 0;
		}
		int av=n-i;
		int rem=m-j;
		if(av<rem) {
			return Integer.MAX_VALUE/2;
		}
		if(dp[i][j]!=-1) {
			return dp[i][j];
		}
		long ans1=sol(i+1,j,n,m,a, zero, one);
		long ans2=Math.abs(zero.get(i)-one.get(j))+sol(i+1,j+1,n,m,a, zero, one);
		dp[i][j]=(int) Math.min(ans1, ans2);
		return dp[i][j];
	}
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
}
