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 static java.lang.Double.parseDouble;
import static java.lang.Integer.max;
import static java.lang.Integer.min;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.StrictMath.abs;
import static java.lang.System.exit;
import static java.util.Arrays.sort;
import java.io.*;
import java.util.*;


public class A {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    static void solve() throws Exception {
        int n = nextInt();
        int a[] = new int[n];
        ArrayList<Integer> z = new ArrayList<Integer>();
        for(int i=0;i<n;i++) {
            a[i] = nextInt();
            if(a[i] == 0) {
                z.add(i);
            }
        }
        int zero[] = new int[z.size()];
        for(int i=0;i<z.size();i++) zero[i] = z.get(i);
        for(int i=0;i<n;i++) {
            if(a[i] == 0) out.print(0 + " ");
            else {
                int lo = min(lower_bound(zero,i),z.size()-1);
                out.print(min(Math.abs(i-zero[lo]),Math.abs(i-zero[lo>0?lo-1:0])) + " ");
            }

        }

    }

    public static int lower_bound(int[] a, int v) {
        int low = -1, high = a.length;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] >= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }


    public static int upper_bound(int[] a, int v) {
        int low = -1, high = a.length;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] > v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }

    static int gcd(int a, int b) { return b==0 ? a : gcd(b, a%b); }


    static int nextInt() throws IOException {
        return parseInt(next());
    }

    static long nextLong() throws IOException {
        return parseLong(next());
    }

    static double nextDouble() throws IOException {
        return parseDouble(next());
    }

    static String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    public static void main(String[] args) {
        try {

            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            long lStartTime = System.currentTimeMillis();
            solve();
            long lEndTime = System.currentTimeMillis();
            //System.out.println("Elapsed time in seconds: " + (double)(lEndTime - lStartTime) / 1000.0);
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            exit(1);
        }
    }
}