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.io.PrintWriter;
import java.util.*;
public class Main{
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }
        long[] nextArray(long n) {
            long[] a = new long[(int) n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
    static class FastWriter extends PrintWriter {
            FastWriter(){
                super(System.out);
            }
            void println(int[] array) {
                for(int i=0; i<array.length; i++) {
                    print(array[i]+" ");
                }
                println();
            }
            void println(long [] array) {
                for(int i=0; i<array.length; i++) {
                    print(array[i]+" ");
                }
                println();
            }
        }
    public static void main(String[] args){
        FastScanner in = new FastScanner();
        FastWriter out = new FastWriter();
        //int t=in.nextInt();
        int t=1;
        while (t-->0){
            int n=in.nextInt();
            int[] ar=in.nextArray(n);
            boolean[] occupied=new boolean[n];
            int cnt=0;
            for (int i = 0; i < n; i++) {
                if(ar[i]==1){
                    occupied[i]=true;
                    cnt++;
                }
            }
            int zero=n-cnt;
            int one=cnt;
            if(cnt==0){
                out.println(0);
            }else {
                cnt=0;
                for (int i = 0; i < n; i++) {
                    if(ar[i]==1){
                        one--;
                        int left=100000,right=100000;
                        int j=i-1;
                        while (j>=0){
                            if(!occupied[j]){
                                left=j;
                                break;
                            }
                            j--;
                        }
                        j=i+1;
                        while (j<n){
                            if(!occupied[j]){
                                right=j;
                                break;
                            }
                            j++;
                        }
                        if(left==100000){
                            cnt+=right-i;
                            occupied[right]=true;
                            zero--;
                        }else if(right==100000){
                            cnt+=i-left;
                            occupied[left]=true;
                        }else {
                            if(one>=zero){
                                cnt+=i-left;
                                occupied[left]=true;
                            }else {
                                if((i-left)<=right-i){
                                    cnt+=i-left;
                                    occupied[left]=true;
                                }else {
                                    cnt+=right-i;
                                    occupied[right]=true;
                                    zero--;
                                }
                            }
                        }
                    }else {
                        zero--;
                    }
                }
                out.println(cnt);
            }
        }
        out.close();
    }
    static int reduceFraction(int x, int y) {
        int d= gcd(x, y);
        return x/d+y/d;
    }
    static boolean subset(int[] ar,int n,int sum){
        if(sum==0){
            return true;
        }
        if(n<0||sum<0){
            return false;
        }
        return subset(ar,n-1,sum)||subset(ar,n-1,sum-ar[n]);
    }
    static boolean isPrime(int n){
        if(n<=1) return false;
        for(int i = 2;i<=Math.sqrt(n);i++){
            if (n % i == 0) return false;
        }
        return true;
    }
    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static boolean isPowerOfTwo(int n) {
        if(n==0||n==1)
            return false;
        return ((int)(Math.ceil((Math.log(n) / Math.log(2)))) == (int)(Math.floor(((Math.log(n) / Math.log(2))))));
    }
    static boolean isPerfectSquare(int x){
        if (x >= 0) {
            int sr = (int)Math.sqrt(x);
            return ((sr * sr) == x);
        }
        return false;
    }
}