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.*;
import java.util.stream.IntStream;

public class Main {

    static long startTime = System.currentTimeMillis();

    // for global initializations and methods starts here

    // global initialisations and methods end here

    static void run(){
    boolean tc = false;
    AdityaFastIO r = new AdityaFastIO();
    //FastReader r = new FastReader();

    try (OutputStream out = new BufferedOutputStream(System.out)) {

        //long startTime = System.currentTimeMillis();

        int testcases = tc ? r.ni() : 1;
        int tcCounter = 1;
        // Hold Here Sparky------------------->>>
        // Solution Starts Here

        start : while (testcases --> 0) {

            int n = r.ni();
            int[] arr = new int[n];
            List<Integer> one = new ArrayList<>();
            List<Integer> zero = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                arr[i] = r.ni();
                if (arr[i] == 1) one.add(i);
                else zero.add(i);
            }
            long[][] dp = new long[n + 2][n + 2];
            for (int i = 1; i <= one.size(); i++)
                dp[i][zero.size() + 1] = (long) (1e15);
            dp[one.size() + 1][zero.size() + 1] = 0;
            for (int i = one.size(); i > 0; i--) {
                for (int j = zero.size(); j > 0; j--) {
                    if (i <= one.size() && j <= zero.size())
                        dp[i][j] = Math.min(Math.abs(one.get(i - 1) - zero.get(j - 1)) + dp[i + 1][j + 1], dp[i][j + 1]);
                }
            }
        }
        // Solution Ends Here
    } catch (IOException e) {
        e.printStackTrace();
    }
}

    static class AdityaFastIO{
        final private int BUFFER_SIZE = 1<<16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        public BufferedReader br;
        public StringTokenizer st;

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

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

        public String word() {
            while (st == null || !st.hasMoreElements()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }

        public String line() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[100000001]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int ni() 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 nl() 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 nd() 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();
        }
    }
    public static void main(String[] args) throws Exception {run();}

    static long mod = 998244353;
    static long modInv(long base, long e) {
    long result = 1;
    base %= mod;
    while (e>0) {
        if ((e & 1)>0) result = result * base % mod;
        base = base * base % mod;
        e >>= 1;
    }
    return result;
}

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); }
        String word() {
            while (st == null || !st.hasMoreElements()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }
        String line() {
            String str = "";
            try { str = br.readLine(); }
            catch (IOException e) { e.printStackTrace(); }
            return str;
        }
        int ni() { return Integer.parseInt(word()); }
        long nl() { return Long.parseLong(word()); }
        double nd() { return Double.parseDouble(word()); }
    }

    static int MOD = (int) (1e9 + 7);

    static long powerLL(long x, long n) {
    long result = 1;
    while (n > 0) {
        if (n % 2 == 1) result = result * x % MOD;
        n = n / 2;x = x * x % MOD;
    }
    return result;
}

    static long powerStrings(int i1, int i2) {
    String sa = String.valueOf(i1);
    String sb = String.valueOf(i2);
    long a = 0, b = 0;
    for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
    for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
    return powerLL(a, b);
}

    static long gcd(long a, long b) { if (a == 0) return b;else return gcd(b % a, a); }
    static long lcm(long a, long b) { return (a * b) / gcd(a, b); }

    static long lower_bound(List<Long> list, long k) {
    int s = 0;
    int e = list.size();
    while (s != e) {
        int mid = (s + e) >> 1;
        if (list.get(mid) < k) s = mid + 1;
        else e = mid;
    }
    if (s == list.size()) return -1;
    return s;
}

    static int upper_bound(List<Long> list, long k) {
    int s = 0;
    int e = list.size();
    while (s != e) {
        int mid = (s + e) >> 1;
        if (list.get(mid) <= k) s = mid + 1;
        else e = mid;
    }
    if (s == list.size()) return -1; return s;
}

    static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
    graph.get(edge1).add(edge2);graph.get(edge2).add(edge1);
}

    public static class Pair implements Comparable<Pair> {
        int first;int second;
        public Pair(int first, int second) { this.first = first;this.second = second; }
        public String toString() { return "(" + first + "," + second + ")"; }
        public int compareTo(Pair o) {
            // TODO Auto-generated method stub
            if(this.first!=o.first)
                return (int) (this.first - o.first);
            else return(int)(this.second-o.second);
        }
    }

    public static class PairC<X,Y> implements Comparable<PairC> {
        X first;Y second;
        public PairC(X first, Y second) { this.first = first;this.second = second; }
        public String toString() { return "(" + first + "," + second + ")"; }
        public int compareTo(PairC o) {
            // TODO Auto-generated method stub
            return o.compareTo((PairC) first);
        }
    }

    static boolean isCollectionsSorted(List<Long> list) {
    if (list.size() == 0 || list.size() == 1) return true;
    for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
    return true;
}

    static boolean isCollectionsSortedReverseOrder(List<Long> list) {
    if (list.size() == 0 || list.size() == 1) return true;
    for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
    return true;
}

}