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 
//Educational Codeforces Round 20
import java.io.*;
import java.util.*;

public class TaskB {
	
	public static void main (String[] args) throws IOException {
		FastScanner fs = new FastScanner(System.in);
		PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
		
		int n = fs.nextInt();
		int[] a = new int[n];
        int[] d = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = fs.nextInt();
        }
        
        int i = 0;
        while (i < n && a[i] != 0) {
            d[i] = Integer.MAX_VALUE;
            i++;
        }

        for (int j = i; j < n; j++) {
            if (a[j] == 0) {
                i = j;
            }
            d[j] = j-i;            
        }

        i = n-1;
        while (i >= 0 && a[i] != 0) {
            i--;
        }

        for (int j = i; j >= 0; j--) {
            if (a[j] == 0) {
                i = j;
            }
            d[j] = Math.min(i-j, d[j]);            
        }

        for (int j = 0; j < n; j++) {
            pw.print(d[j]);
            pw.print(" ");
        }

        pw.println();		
        		
		pw.close();		
	}
	
	static class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;        
        FastScanner(InputStream i) {
            reader = new BufferedReader(new InputStreamReader(i));
            tokenizer = new StringTokenizer("");
        }
        String next() throws IOException {
            while(!tokenizer.hasMoreTokens()) tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }        
    }
}