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 java.io.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class PracticeA {
    public static PrintWriter out;
    public static FastScanner in;

    private void solve() {
        int n = in.nextInt();

        int[] a = new int[n+1];
        for(int i=1;i<=n;i++){
            a[i] = in.nextInt();
        }

        int[] left = new int [n+1];
        Arrays.fill(left,Integer.MAX_VALUE);

        for(int i=1;i<=n;i++){
            if(a[i] == 0){
                left[i] = 0;
            }
            left[i] = left[i-1] == Integer.MAX_VALUE?Math.min(left[i],left[i-1]):Math.min(left[i],left[i-1]+1);
        }

        int[] right = new int [n+1];
        Arrays.fill(right,Integer.MAX_VALUE);
        right[n] = a[n] == 0?0:right[n];

        for(int i=n-1;i>0;i--){
            if(a[i] == 0){
                right[i] = 0;
            }
            right[i] = right[i+1] == Integer.MAX_VALUE?Math.min(right[i],right[i+1]):Math.min(right[i],right[i+1]+1);
        }

        for(int i=1;i<=n;i++){
            out.print(Math.min(left[i],right[i])+" ");
        }
        out.println();
    }

    private void runIO() {
        in = new FastScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        solve();
        out.close();
    }

    private static class FastScanner {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        private FastScanner() {
            bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        }

        private String next() {
            if (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

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

        private long nextLong() {
            return Long.parseLong(next());
        }

        private String nextLine() {
            String ret = "";
            try {
                ret = bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return ret;
        }
    }

    public static void main(String[] args) {
        new PracticeA().runIO();
    }
}
