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.util.*;
import java.io.*;

public class B {

    int a[], prev[], suf[];

    int INF = 1000000;

    int getPrev(int n) {
        return prev[n + 1];
    }

    int getSuf(int n) {
        return suf[n];
    }

    public void solve() throws IOException {
        int n = nextInt();
        a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();

        prev = new int[n + 1];
        suf = new int[n + 1];

        prev[0] = INF;
        for (int i = 1; i <= n; i++) {
            if (a[i - 1] == 0)
                prev[i] = 0;
            else
                prev[i] = prev[i - 1] + 1;
        }

        suf[n] = INF;
        for (int i = n - 1; i >= 0; i--) {
            if (a[i] == 0)
                suf[i] = 0;
            else
                suf[i] = suf[i + 1] + 1;
        }

        for (int i = 0; i < n; i++) {
            output.print(Math.min(getPrev(i), getSuf(i)) + " ");
        }
    }

    public BufferedReader input;
    public PrintWriter output;
    public StringTokenizer stringTokenizer = new StringTokenizer("");

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

    B() throws IOException {
        input = new BufferedReader(new InputStreamReader(System.in));
        output = new PrintWriter(System.out);
        solve();
        input.close();
        output.close();
    }

    public String next() throws IOException {
        while (!stringTokenizer.hasMoreTokens() || stringTokenizer == null)
            stringTokenizer = new StringTokenizer(input.readLine());

        return stringTokenizer.nextToken();
    }

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

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

    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}