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 SolutionC{
       public static void main(String[] args) throws Exception{
               Fast sc=new Fast();
       StringBuilder sb=new StringBuilder();
        PrintWriter out=new PrintWriter(System.out);
       
         int n=sc.nextInt();
         int[] ar=new int[n];
         ArrayList<Integer> one=new ArrayList<>();
         ArrayList<Integer> z=new ArrayList<>();
         for(int i=0;i<n;i++){
          ar[i]=sc.nextInt();
          if(ar[i]==1)one.add(i);
          else z.add(i);
         }
         if(one.size()==0)out.println(0);
         else{
            Collections.sort(one);
            Collections.sort(z);
            long ans=0;
            int[] vis=new int[z.size()];
            for(int i=0;i<one.size();i++){
              int max=10000000;
              int pos=0;
              for(int j=0;j<z.size();j++){
                  if(vis[j]==0){
                    int val=Math.abs(one.get(i)-z.get(j));
                    if(val<max){
                      max=val;
                      pos=j;
                    }
                  }
              }
              ans+=(long)max;
              vis[pos]=1;
            }
            out.println(ans);
         }

       
           
           out.close();
}

static void ReverSort(int[] ar){
    ArrayList<Integer> al=new ArrayList<>();
    for(int i=0;i<ar.length;i++){
        al.add(ar[i]);
    }

    Collections.sort(al);
      int j=0;
    for(int i=al.size()-1;i>=0;i--){

        ar[j]=al.get(i);
        j++;
    }
}
static void Sort(int[] ar){
    ArrayList<Integer> al=new ArrayList<>();
    for(int i=0;i<ar.length;i++){
        al.add(ar[i]);
    }

    Collections.sort(al);
      int j=0;
    for(int i=0;i<al.size();i++){

        ar[j]=al.get(i);
        j++;
     }
  }

static int gcd(int a,int b){
    if(b==0) return a;
    else return  gcd(b,a%b);
}
}

class Pair{
    int x, y;
     Pair(int x,int y){
        this.x=x;
        this.y=y;
     }
}

class Fast{
  BufferedReader br; 
  StringTokenizer st;
  public Fast(){ 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; 
        } 
}
    
