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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	
	static final int INF = (int) 1e9 * 2;
	
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		
		TreeSet<Integer> set = new TreeSet<Integer>();
		
		int arr[] = new int[n];
		for(int i = 0; i < n; ++i) {
			arr[i] = sc.nextInt();
			if(arr[i] == 0)
				set.add(i);
		}
		
		for(int i = 0; i < n; ++i) {
			if(arr[i] == 0) continue;
			else {
				Integer bef = set.lower(i);
				Integer aft = set.higher(i);
				if(bef == null)
					bef = -INF;
				if(aft == null)
					aft = INF;
				arr[i] = Math.min(i - bef, aft - i);
			}
		}
		
		for(int i = 0; i < n; ++i) out.print(arr[i] + " ");
		out.println();
		
		out.flush();
		out.close();
	}

	static class Scanner{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public Scanner(FileReader r){	br = new BufferedReader(r);}

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

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

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

		public String nextLine() throws IOException {return br.readLine();}

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

		public boolean ready() throws IOException {return br.ready();}
	}
	
	static boolean OJ = System.getProperty("ONLINE_JUDGE") != null;
	static void tr(Object... o) {
		if(!OJ)	System.out.println(Arrays.deepToString(o));
	}
}