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.*;
import java.util.*;
import java.math.*;
 
public class Edu20Q2
{
    public static void main(String[] args) throws IOException
    {
        FastScanner obj = new FastScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
		
		int n = obj.nextInt();
		int[] arr = new int[n+2];
		for(int i=1;i<=n;i++)
			arr[i] = obj.nextInt();
		int[] ans = new int[n+2];
		
		ans[0] = 1000000;
		for(int i=1;i<=n;i++)
		{
			ans[i] = ans[i-1]+1;	
			if(arr[i] == 0)
				ans[i] = 0;
		}
		ans[n+1] = 1000000;
		for(int i=n;i>=1;i--)
		{
			ans[i] = Math.min(ans[i],ans[i+1]+1);
			if(arr[i] ==0)
				ans[i] = 0;
		}
		for(int i=1;i<=n;i++)
			out.print(ans[i]+" ");
		
        out.close();
   }
   

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------FastScanner class for faster input----------
   public static class FastScanner {
        BufferedReader br;
        StringTokenizer tokenizer;
 
        public FastScanner() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = new StringTokenizer(br.readLine().trim());
        }
 
        String next() {
            while (tokenizer == null || !tokenizer.hasMoreElements()) {
                try {
                    tokenizer = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                    }
            }
          return tokenizer.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
      
        int[] nextIntArray() throws IOException {
            String[] line = br.readLine().trim().split(" ");
            int[] out = new int[line.length];
            
            for (int i = 0; i < line.length; i++) {
                out[i] = Integer.valueOf(line[i]);
            }
            return out;
        }
        
        BigInteger nextBigInteger() throws IOException {
            return new BigInteger(next());
        }
        
        String nextLine(){
            String str = "";
	        try {
	            str = br.readLine();
	        } catch (IOException e) {
	            e.printStackTrace();
	        }
	        return str;
        }

   }
   //--------------------------------------------------------
}