You are given the array of integer numbers a0, a1, ..., an - 1. For each element find the distance to the nearest zero (to the element which equals to zero). There is at least one zero element in the given array.

Input

The first line contains integer n (1 ≤ n ≤ 2·105) — length of the array a. The second line contains integer elements of the array separated by single spaces ( - 109 ≤ ai ≤ 109).

Output

Print the sequence d0, d1, ..., dn - 1, where di is the difference of indices between i and nearest j such that aj = 0. It is possible that i = j.

Examples

Input

9
2 1 0 3 0 0 3 2 4


Output

2 1 0 1 0 0 1 2 3 

Input

5
0 1 2 3 4


Output

0 1 2 3 4 

Input

7
5 6 0 1 -2 3 4


Output

2 1 0 1 2 3 4 
import javax.print.attribute.IntegerSyntax;
import java.sql.Array;
import java.util.*;
import java.io.*;
import static java.lang.Math.*;
public class MainS {
    static final long MOD = 1_000_000_007, INF = 1_000_000_000_000_000_000L;
    static final int INf = 1_000_000_000;
    static FastReader reader;
    static PrintWriter writer;

    public static void main(String[] args) {
        Thread t = new Thread(null, new O(), "Integer.MAX_VALUE", 100000000);
        t.start();
    }

    static class O implements Runnable {
        public void run() {
            try {
                magic();
            } catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }

    public 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;
        }

    }

    static void magic() throws IOException {
        reader = new FastReader();
        writer = new PrintWriter(System.out, true);
        int n = reader.nextInt();
        int arr[] = new int[n];
        for(int i=0;i<n;++i) {
            arr[i] = reader.nextInt();
        }
        int left_min_dis[] = new int[n];
        int right_min_dis[] = new int[n];
        Arrays.fill(left_min_dis, Integer.MAX_VALUE);
        Arrays.fill(right_min_dis, Integer.MAX_VALUE);
        int last_zero = -1;
        for(int i=0;i<n;++i) {
            if(arr[i]==0) {
                last_zero = i;
            }
            if(last_zero!=-1) {
                left_min_dis[i] = i-last_zero;
            }
        }
        last_zero = -1;
        for(int i=n-1;i>=0;--i) {
            if(arr[i]==0) {
                last_zero = i;
            }
            if(last_zero!=-1) {
                right_min_dis[i] = last_zero-i;
            }
        }
        StringBuilder fast = new StringBuilder();
        for(int i=0;i<n;++i) {
            int min = min(left_min_dis[i], right_min_dis[i]);
            fast.append(min);
            fast.append(" ");
        }
        writer.println(fast);
    }
}