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.util.*;
import java.io.*;
import java.math.BigInteger;

public class Tester
{
	public static long mod=(long)(1e9+7);
	public static long xx,yy,d;
	static int minPrime[];
	static boolean isPrime[];
	
	public static void main(String[] args) throws IOException 
	{
		InputReader s=new InputReader(System.in);
        OutputStream outputStream = System.out;
        PrintWriter out=new PrintWriter(outputStream);
        
        int n = s.nextInt();
        int a[] = new int[n]; 
        
        for(int i=0; i<n; i++)
        	a[i] = s.nextInt();
        
        ArrayList<Integer> pos = new ArrayList<>();
        
        for(int i=0; i<n; i++)
        {
        	if(a[i] == 0)
        		pos.add(i);
        }
        
        //debug(pos);
        
        int k = 0;
        
        for(int i=0; i<n; i++)
        {
        	int dis = 0;        	
        	if(a[i] == 0)
        	{
        		if(k != pos.size()-1)
        			k++;
        		System.out.print("0 ");
        	}
        	else
        	{
        		if(k == 0)
        		{
        			dis = Math.abs(pos.get(k) - i);
        		}
        		else
        		{
        			int dis1 = Math.abs(pos.get(k-1) - i);
        			int dis2 = Math.abs(pos.get(k) - i);
        			dis = Math.min(dis1, dis2);
        		}
        		System.out.print(dis+" ");
        	}
        }
        
        
        out.close();
	}  
	
	static void modifiedSieve(int n)
	{
		minPrime = new int[n+1];
		
		for(int i=2; i<=Math.sqrt(n); i++)
		{
			if(minPrime[i] == 0)
			{
				for(int j=i*i; j<=n; j=j+i)
				{
					if(minPrime[j] == 0)
						minPrime[j] = i;
				}
			}
		}
		
		for(int i=2; i<=n; i++)
		{
			if(minPrime[i] == 0)
				minPrime[i] = i;
		}
		
	}
	
	static void Sieve(int n)
	{
		isPrime = new boolean[n+1];
		Arrays.fill(isPrime, true);
		
		isPrime[0]=false;
		isPrime[1]=false;
		
		for(int i=2; i<=Math.sqrt(n); i++)
		{
			if(isPrime[i])
			{
				for(int j=i*i; j<=n; j=j+i)
					isPrime[j]=false;
			}
		}
		
	}
	
	static void extendedEuclid(long A, long B)
	{
		if(B == 0) {
	        d = A;
	        xx = 1;
	        yy = 0;
	    }
	    else {
	        extendedEuclid(B, A%B);
	        long temp = xx;
	        xx = yy;
	        yy = temp - (A/B)*yy;
	    }
	}
	
	static long gcd(long a,long b)
	{
		if(b==0)
			return a;
		
		return gcd(b,a%b);
	}
	
	static long modulo(long x,long y,long p)	
	{
		 long res = 1;
		 x = x % p;  
		 
	    while (y > 0)
	    {
	        if (y%2==1)
	            res = (res*x) % p;
	 
	        y = y>>1;
	        x = (x*x) % p;  
	    }
	    return res;
	}
	
	public static void debug(Object... o)
	{
		System.out.println(Arrays.deepToString(o));
	}
	
	static long exp(long a, long b)
	{
		if(b==0)
			return 1;
		if(b==1)
			return a;
		if(b==2)
			return a*a;

		if(b%2==0)
			return exp(exp(a,b/2),2);
		else
			return a*exp(exp(a,(b-1)/2),2);
	}

	static class Pair implements Comparable<Pair>
	{
		long x,y;
		Pair(long ii, long cc)
		{
			x=ii;
			y=cc;
		}
		
		public int compareTo(Pair o) 
		{
			if(Long.compare(this.x, o.x) != 0)
				return Long.compare(this.x, o.x);
			else
				return Long.compare(this.y, o.y);
		}
		
		public int hashCode() {
			int hu = (int) (x ^ (x >>> 32));
			int hv = (int) (y ^ (y >>> 32));
			return 31 * hu + hv;
		}
 
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return x == other.x && y == other.y;
		}
		
		public String toString() {
			return "[x=" + x + ", y=" + y + "]";
		}
		
	}

    static final class InputReader{
        private final InputStream stream;
        private final byte[] buf=new byte[1024];
        private int curChar;
        private int Chars;
        public InputReader(InputStream stream){this.stream=stream;}
        private int read()throws IOException{
            if(curChar>=Chars){
                curChar=0;
                Chars=stream.read(buf);
                if(Chars<=0)
                    return -1;
            }
            return buf[curChar++];
        }
        public final int nextInt()throws IOException{return (int)nextLong();}
        public final long nextLong()throws IOException{
            int c=read();
            while(isSpaceChar(c)){
                c=read();
                if(c==-1) throw new IOException();
            }
            boolean negative=false;
            if(c=='-'){
                negative=true;
                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 negative?(-res):(res);
        }
        public final int[] nextIntBrray(int size)throws IOException{
            int[] arr=new int[size];
            for(int i=0;i<size;i++)arr[i]=nextInt();
            return arr;
        }
        public final String nextString()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(!isSpaceChar(c));
            return res.toString();
        }
        public final String nextLine()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(c!='\n' && c!=-1);
            return res.toString();
        }
        private boolean isSpaceChar(int c)
        {
            return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
        }
    }
 
}