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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solver {

    public static void main(String[] args) throws IOException {
        new Solver().read();
    }

    static FastScanner in = new FastScanner();
    static PrintWriter out;
    static int n;
    static int a[];
    void read() throws IOException {
        out = new PrintWriter(System.out);
        int test = 1;
        while (test-- > 0) {
            n = in.nextInt();
            a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }
            solve();
        }
        out.close();
    }


    void solve() throws IOException {
       long pref[] = new long[n];
       long suf[] = new long[n];
       long first = Integer.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            if(a[i] == 0){
                pref[i] = 0;
                first = i;
            }else{
                pref[i] = i - first;
            }
        }
        first = Integer.MAX_VALUE;
        for (int i = n - 1; i >= 0; i--) {
            if(a[i] == 0){
                suf[i] = 0;
                first = i;
            }else{
                suf[i] = first - i;
            }
        }
        for (int i = 0; i < n; i++) {
            System.out.print(Math.min(pref[i],suf[i]) + " ");
        }
    }
}


class FastScanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");

    String next() throws IOException {
        while (!st.hasMoreElements()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

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

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