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.*;
import java.lang.*;
import static java.lang.Math.*;
 
public class Sol
{
    
    static long mod=1000000007;
    
    static int a[];
    
    static void initialize(int n)
    {
        for(int i=0;i<=n;i++)
            a[i]=i;
    }
    
    static int root(int r)
    {
        while(r!=a[r])
            r=a[r];
        
        return r;
    }
    
    static void union(int u,int v)
    {
        int r1=root(u);
        int r2=root(v);
        
        a[r1]=r2;
    }
    
    
    public static void main(String args[]) throws Exception
    {
        InputReader in;
        PrintWriter w;
        boolean online = false;
        String fileName = "input";

        if (online) 
        {
            in = new InputReader(new FileInputStream(new File(fileName + ".in")));
            w = new PrintWriter(new FileWriter("out.txt"));
        } 
        else 
        {
            in = new InputReader(System.in);
            w = new PrintWriter(System.out);
        }





            int n=in.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=in.nextInt();
            }
            int prev=-1;
            int ans[]=new int[n];
        for(int i=0;i<n;i++){
            ans[i]=Integer.MAX_VALUE;
        }
            for(int i=0;i<n;i++)
            {
                
                if(a[i]==0){
                    prev=i;
                    ans[i]=0;
                }
                
                if(a[i]!=0)
                {
                    if(prev!=-1)
                    ans[i]=abs(i-prev);
                    
                }
                
            }
            prev=-1;
            for(int i=n-1;i>=0;i--){
                
                if(a[i]==0){
                    ans[i]=0;
                    prev=i;
                }
                else{
                    
                    if(prev!=-1)ans[i]=min(ans[i],abs(i-prev));
                    
                    
                    
                }
                
            }
            for(int i=0;i<n;i++)w.print(ans[i]+" ");
            
        w.close();
    }
    
    
    private static long gcd(long a, long b)
    {
        while (b > 0)
        {
            long temp = b;
            b = a % b; // % is remainder
            a = temp;
        }
        return a;
    }
 
    private static long gcd(long[] input)
    {
        long result = input[0];
        
        for(int i = 1; i < input.length; i++) 
            result = gcd(result, input[i]);
        
        return result;
    }
    
    private static long lcm(long a, long b)
    {
        return a * (b / gcd(a, b));
    }
 
    private static long lcm(long[] input)
    {
        long result = input[0];
        
        for(int i = 1; i < input.length; i++) 
            result = lcm(result, input[i]);
        
        return result;
    }
    
    public static void Array_2dsort(Integer[][] a)
    {
        Arrays.sort(a, new Comparator<Integer[]>() 
        {
            public int compare(Integer[] int1, Integer[] int2) 
            {
                Integer numOfKeys1 = int1[1];       //about which column u want to sort
                Integer numOfKeys2 = int2[1];
                return numOfKeys1.compareTo(numOfKeys2);
            }
        });
    }
     
    static long powmod(long x,long n,long m)        //(a/b)%mod = (a * (b^(m-2))%mod  here --> x=a, n=mod-2, m=mod  
    {
	if (n == 0)
            return 1;
        else if (n%2==0)
            return powmod(((x%m)*(x%m))%m,n/2,m);
	else if(n%2==1)
            return (((x%m)*powmod(((x%m)*(x%m))%m,(n-1)/2,m))%m);
	else
            return 0;
    }
        
	
	static class InputReader
	{
	
                private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try 
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			return buf[curChar++];
		}
	 
		public String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			int c = read();
			
			while(isSpaceChar(c)) 
				c = read();
			
			int sgn = 1;
			
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			do 
			{
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
			
			return res * sgn;
		}
		
		public long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    
}