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.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public final class Solution {

    static int solve(ArrayList<Integer> filled,ArrayList<Integer> unfilled, int i, int j,int ans,int min,int[][] dp){
           if(i!=filled.size() && j==unfilled.size()){
           
            return Integer.MAX_VALUE;
        }
        if(i==filled.size() || j==unfilled.size()){
            min=Math.min(min,ans);

            // System.out.println(min);
            return min;
        }
            int val=Integer.MAX_VALUE;
           ans+=Math.abs(filled.get(i)-unfilled.get(j));
          if(dp[i+1][j+1]!=-1){
              return dp[i+1][j+1];
          }else{
              val= solve(filled,unfilled,i+1,j+1,ans,min,dp);
              dp[i+1][j+1]=val;
          }
         int val2=Integer.MAX_VALUE;
         
          ans-=Math.abs(filled.get(i)-unfilled.get(j));
          if(dp[i][j+1]!=-1){
              return dp[i][j+1];
          }else{
              if( j+1<unfilled.size()){
        val2= solve(filled,unfilled,i,j+1,ans,min,dp);
                 dp[i][j+1]=val2;
        }
          }
     
        
        
        return Math.min(val2,val)  ;

    }

    
    public static void main(String[] args) throws Exception {
        
        Reader sc = new Reader();
        BufferedWriter op = new BufferedWriter(new OutputStreamWriter(System.out));
         
         int n=sc.nextInt();
          ArrayList<Integer> fill= new ArrayList<Integer>();
          ArrayList<Integer> unfilled= new ArrayList<>();
          for(int i=0;i<n;i++){
              int x =sc.nextInt();
              if(x==1){
                  fill.add(i);
              }else{
                  unfilled.add(i);
              }
          }
          int[][] dp =new int[n][n];
          for(int i=0;i<n;i++){
              for(int j=0;j<n;j++){
                  dp[i][j]=-1;
              }
          }

          if(fill.size()==0){
              System.out.println(0);
              
          }else{
   int min=Integer.MAX_VALUE;
          int ans=solve(fill,unfilled,0,0,0,min,dp);
         System.out.println(ans);
          }
           
        op.flush();
    }




   
    }

class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') {
                if (cnt != 0) {
                    break;
                } else {
                    continue;
                }
            }
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (c == '.') {
            while ((c = read()) >= '0' && c <= '9') {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null)
            return;
        din.close();
    }
}
// BufferedWriter output = new BufferedWriter(
// new OutputStreamWriter(System.out));

// while(t-->0){
// int k=sc.nextInt();
// int [] arr= new int[(2*k)+1];

// int ans = 0;
// System.out.println(k+"=> ");
// for(int i=(2*k);i<(4*k)+1;i++){
// int one =k+(i*i);
// int two=k+((i+1)*(i+1));
// int val = gcd(one,two);
// System.out.print("["+i+" "+"("+one+"-"+two+") =>"+val+" diff=> "+(two-one)+"
// ]");
// ans+=val;

// }
// System.out.println();
// System.out.println();
// // op.write(ans+"\n");
// }
