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.*;
import java.util.*;
public class Main {
    static ArrayList<Integer> one=new ArrayList<>();
    static ArrayList<Integer> zero=new ArrayList<>();
    static long dp[][]= new long[5001][5001];
    static long solve(int i,int j){
        if (i==one.size())return 0;
        if (j==zero.size())return Integer.MAX_VALUE;
        if (dp[i][j]!=-1){
           return dp[i][j];
        }
        return dp[i][j]=Math.min(solve(i+1,j+1)+Math.abs(one.get(i)-zero.get(j)),solve(i,j+1));
    }

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
//        int t=sc.nextInt();
//        while (t-->=1){
            int n=sc.nextInt();
            int a[]=sc.readArray(n);
            for (long i[]:dp){
                Arrays.fill(i,-1);
            }
            for (int i=0;i<n;i++){
                if (a[i]==1)one.add(i);
                else zero.add(i);
            }
            Collections.sort(one);
            Collections.sort(zero);
        System.out.println(solve(0,0));




    }


//        out.flush();



    //------------------------------------if-------------------------------------------------------------------------------------------------------------------------------------------------
    //sieve
    static void primeSieve(int a[]){
        //mark all odd number as prime
        for (int i=3;i<a.length;i+=2){
            a[i]=1;
        }
        for (long i=3;i<a.length;i+=2){
            //if the number is marked then it is prime
            if (a[(int) i]==1){
                //mark all muliple of the number as not prime
                for (long j=i*i;j<a.length;j+=i){
                    a[(int)j]=0;

                }
            }
        }
        a[2]=1;
        a[1]=a[0]=0;
    }
    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    static String sortString(String s) {
        char temp[] = s.toCharArray();
        Arrays.sort(temp);
        return new String(temp);
    }
    static class Pair implements Comparable<Pair> {
        String a;
        int b;

        public Pair(String a, int b) {
            this.a = a;
            this.b = b;
        }
        //        to sort first part
//        public int compareTo(Pair other) {
//            if (this.a == other.a) return other.b > this.b ? -1 : 1;
//            else if (this.a > other.a) return 1;
//            else return -1;
//        }
        public int compareTo(Pair other) {
//            if (this.b == other.b) return 0;
            if (this.b > other.b) return 1;
            else return -1;
        }
        //sort on the basis of first part only
//        public int compareTo(Pair other) {
//            if (this.a == other.a) return 0;
//            else if (this.a > other.a) return 1;
//            else return -1;
//        }

    }
    static int[] frequency(String s){
        int fre[]= new int[26];
        for (int i=0;i<s.length();i++){
            fre[s.charAt(i)-'a']++;
        }
        return fre;
    }
    static long LOWERBOUND(long a[],long k){
        int s=0,e=a.length-1;
        long ans=-1;
        while (s<=e){
            int mid=(s+e)/2;
            if (a[mid]<=k){
                ans=mid;
                s=mid+1;
            }
            else {
                e=mid-1;
            }
        }
        return ans;
    }
    static long mod =(long)(1e9+7);
    static long mod(long x) {
        return ((x % mod + mod) % mod);
    }
    static long div(long a,long b){
        return ((a/b)%mod+mod)%mod;
    }
    static long add(long x, long y) {
        return mod(mod(x) + mod(y));
    }
    static long mul(long x, long y) {
        return mod(mod(x) * mod(y));
    }
    //Fast Power(logN)
    static int fastPower(long a,long n){
        int ans=1;
        while (n>0){
            long lastBit=n&1;
            if (lastBit==1){
                ans=(int)mul(ans,a);
            }

            a=(int)mul(a,a);
            n>>=1;
        }
        return ans;
    }
    static int[] find(int n, int start, int diff) {
        int a[] = new int[n];
        a[0] = start;
        for (int i = 1; i < n; i++) a[i] = a[i - 1] + diff;
        return a;
    }
    static void swap(int a, int b) {
        int c = a;
        a = b;
        b = c;
    }
    static void printArray(int a[]) {
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
    }
    static boolean sorted(int a[]) {
        int n = a.length;
        boolean flag = true;
        for (int i = 0; i < n - 1; i++) {
            if (a[i] > a[i + 1]) flag = false;
        }
        if (flag) return true;
        else return false;
    }
    public static int findlog(long n) {
        if (n == 0)
            return 0;

        if (n == 1)
            return 0;
        if (n == 2)
            return 1;
        double num = Math.log(n);
        double den = Math.log(2);
        if (den == 0)
            return 0;
        return (int) (num / den);
    }
    public static long gcd(long a, long b) {
        if (b % a == 0)
            return a;
        return gcd(b % a, a);
    }
    public static int gcdInt(int a, int b) {

        if (b % a == 0)
            return a;

        return gcdInt(b % a, a);

    }
    static void sortReverse(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        //        Collections.sort.(l);
        Collections.sort(l, Collections.reverseOrder());
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    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[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readArrayLong(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());
        }
    }
}