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 Solution
{
    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; 
        } 
    }
    static final long mod=(long)1e9+7;
    public static long pow(long a,int p)
    {
        long res=1;
        while(p>0)
        {
            if(p%2==1)
            {
                p--;
                res*=a;
                res%=mod;
            }
            else
            {
                a*=a;
                a%=mod;
                p/=2;
            }
        }
        return res;
    }
    static class Pair
    {
        int u,v,w;
        Pair(int u,int v,int w)
        {
            this.u=u;
            this.v=v;
            this.w=w;
        }
    }
    /*static class Pair implements Comparable<Pair>
    {
        int v,l;
        Pair(int v,int l)
        {
            this.v=v;
            this.l=l;
        }
        public int compareTo(Pair p)
        {
            return l-p.l; 
        }
    }*/
    static int gcd(int a,int b)
    {
        if(b%a==0)
        return a;
        return gcd(b%a,a);
    }
    public static void dfs(int u,int dist[],int sub[],int mxv[],int par[],ArrayList<Integer> edge[])
    {
        sub[u]=1;
        for(int v:edge[u])
        {
            if(dist[v]==-1)
            {
                par[v]=u;
                dist[v]=dist[u]+1;
                dfs(v,dist,sub,mxv,par,edge);
                if(sub[v]+1>sub[u])
                {
                    sub[u]=sub[v]+1;
                    mxv[u]=v;
                }
            }
        }
    }
    public static void main(String args[])throws Exception
    {
        FastReader fs=new FastReader();
        PrintWriter pw=new PrintWriter(System.out);
        //int tc=fs.nextInt();
        int n=fs.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++)
        a[i]=fs.nextInt();
        ArrayList<Integer> o=new ArrayList<>();
        ArrayList<Integer> z=new ArrayList<>();
        for(int i=0;i<n;i++)
        {
            if(a[i]==1)o.add(i);
            else z.add(i);
        }
        int ans[][]=new int[o.size()+1][z.size()+1];
        for(int i=1;i<=o.size();i++)
        {
            for(int j=i;j<=z.size();j++)
            {
                if(i==j)ans[i][j]=ans[i-1][j-1]+(int)Math.abs(o.get(i-1)-z.get(j-1));
                else 
                ans[i][j]=Math.min(ans[i][j-1],ans[i-1][j-1]+(int)Math.abs(o.get(i-1)-z.get(j-1)));
            }
        }
        pw.println(ans[o.size()][z.size()]);
        pw.flush();
        pw.close();
    }
}