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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collectors;


public class Solution {


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

    static long [][] dp;

    public static long rec(int i, int j, MyList<Integer> ones, MyList<Integer> zero, int o, int z) {
        if(i == o) {
            return 0;
        } if(j == z) {
            return 100000000;
        }
        if(dp[i][j] != -1) return dp[i][j];
        long res = Math.min(Math.abs(ones.get(i) - zero.get(j)) + rec(i + 1, j + 1, ones, zero, o, z), rec(i, j + 1, ones, zero, o, z));
        dp[i][j] = res;
        return res;
    }
    public static void solve() {
        dp = new long[5000][5000];
        for(int i = 0; i < 5000; ++i) {
            for(int j = 0; j < 5000; ++j) {
                dp[i][j] = -1;
            }
        }
        int n = scanner.nextInt();
        MyList<Integer> myList1 = new MyList<Integer>(0) {
            @Override
            Integer getInput(int index) {
                return null;
            }
        };
        MyList<Integer> myList2 = new MyList<Integer>(0) {
            @Override
            Integer getInput(int index) {
                return null;
            }
        };
        int z = 0, o = 0;
        for(int i = 0; i < n; ++i) {
            int k = scanner.nextInt();
            if(k==1) {
                myList2.list.add(i);
                ++o;
            } else{
                myList1.list.add(i);
                ++z;
            }
        }
        System.out.println(rec(0, 0, myList2, myList1, o, z));
    }

    private static FastReader scanner;

    static class Pair implements Comparable {
        Integer index, value;

        public Pair(Integer index, Integer value) {
            this.index = index;
            this.value = value;
        }

        public Integer getIndex() {
            return index;
        }

        public void setIndex(int index) {
            this.index = index;
        }

        public Integer getValue() {
            return value;
        }

        public void setValue(Integer value) {
            this.value = value;
        }

        @Override
        public int compareTo(Object p) {
            return this.getValue().compareTo(((Pair) p).getValue());
        }
    }

    abstract static class MyList<E> {
        public ArrayList<E> list;

        public MyList(int size) {
            list = new ArrayList<>();
            for(int i = 0; i < size; ++i){
                list.add(null);
            }
        }

        public int size() {
            return list.size();
        }


        public E get(int i) {
            return list.get(i);
        }

        public void set(int i, E val) {
            list.set(i, val);
        }

        public void getInput() {
            for(int i = 0; i < size(); ++i) {
                list.set(i, getInput(i));
            }
        }

        public void printArray() {
            for(int i = 0; i < list.size(); ++i) {
                System.out.print(list.get(i).toString());
                if(i != list.size() - 1)
                    System.out.print(" ");
                else
                    System.out.println();
            }
        }

        abstract E getInput(int index);
    }

    public static void main(String[] args) {
        scanner = new FastReader();
        int t = 1;
        //t = scanner.nextInt();
        for(int i = 0; i < t; ++i) {
            solve();
        }
    }

    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;
        }
    }
}