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.*;


public class Problems2 {
    
    public static void main(String[] args) throws IOException {
        FastScanner sc=new FastScanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        int ans[]=new int[n];
        Arrays.fill(ans, 10000000);
        for(int i=0;i<n;i++){
            a[i]=sc.nextInt();
        }
        int z=0;
        for(int i=0;i<n;i++){
            if(a[i]==0){
                z=i;
                break;
            }
        }
        for(int i=z;i<n;i++){
            if(a[i]==0)z=i;
            ans[i]=i-z;
        }
        for(int i=z;i>=0;i--){
            if(a[i]==0)z=i;
            ans[i]=(z-i<ans[i])?z-i:ans[i];
        }
        dis(ans);
        
        
        
    }
    public static void dis(int a[]){
        StringBuilder s=new StringBuilder();
        for(int i=0;i<a.length;i++){
            s.append(a[i]+" ");
        }
        System.out.println(s.toString());
    }
    


//_________________________________
    static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
		
	    public FastScanner(InputStream i) {
	        br = new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
				
	    public String next() throws IOException {
	        if(st.hasMoreTokens())
	            return st.nextToken();
	        else
	            st = new StringTokenizer(br.readLine());
	        return next();
	    }

	    public int nextInt() throws IOException {
	        return Integer.parseInt(next());
	    }
	    //#
	    public long nextLong() throws IOException {
	        return Long.parseLong(next());
	    }
	    public double nextDouble() throws IOException {
	        return Double.parseDouble(next());
	    }
	    //$
	}
}
