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.util.StringTokenizer;

public class Main
{

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        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;
        }
    }

    public static void main(String[] args)
    {
        setup();
        xuly();
    }

    private static int n;
    private static int[] a, d;

    private static void setup() {
        FastReader fastReader = new FastReader();
        n = fastReader.nextInt();
        a = new int[n];
        d = new int[n];
        for (int i = 0; i < n; i ++)
            a[i] = fastReader.nextInt();
    }

    private static void xuly()
    {
        int lastZero = Integer.MIN_VALUE / 2;
        for (int i = 0; i < n; i ++){
            if (a[i] == 0)
                lastZero = i;
            d[i] = i - lastZero;
        }

        lastZero = Integer.MAX_VALUE / 2;
        for (int i = n - 1; i >= 0; i --)
        {
            if (a[i] == 0)
                lastZero = i;
            d[i] = Integer.min(d[i], lastZero - i);
        }

        for (int i = 0; i < n; i ++)
            System.out.print(d[i] + " ");
    }
}
