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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class P803B
{
	public static void main(String[] args)
	{
		FastScanner scan = new FastScanner();
		int n = scan.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = scan.nextInt();
		TreeSet<Integer> set = new TreeSet<>();
		for (int i = 0; i < n; i++)
		{
			if (arr[i] == 0)
				set.add(i);
		}
		PrintWriter pw = new PrintWriter(System.out);
		for (int i = 0; i < n; i++)
		{
			if (i > 0)
				pw.print(" ");
			int d1 = Integer.MAX_VALUE;
			int d2 = Integer.MAX_VALUE;
			Integer lo = set.floor(i);
			if (lo != null)
				d1 = Math.abs(i-lo);
			Integer hi = set.higher(i);
			if (hi != null)
				d2 = Math.abs(i-hi);
			pw.print(Math.min(d1, d2));
		}
		pw.flush();
	}
	
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			try
			{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
		}

		public String next()
		{
			if (st.hasMoreTokens())
				return st.nextToken();
			try
			{
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return st.nextToken();
		}

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

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

		public String nextLine()
		{
			String line = "";
			try
			{
				line = br.readLine();
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return line;
		}
	}
}
