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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.math.*;
  
public class er10a
{ 
    //By shwetank_verma
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
    static int mod=(int)(1e9+7);
    static boolean primes[]=new boolean[1000007];
    static ArrayList<Integer> b=new ArrayList<>();
    static void seive(int n){
        Arrays.fill(primes,true);
        primes[0]=primes[1]=false;
        for(int i=2;i*i<=n;i++){
            if(primes[i]==true){
                for(int p=i*i;p<=n;p+=i){
                    primes[p]=false;
                }
            }
        }
        if(n<1000007){
        	for(int i=2;i<=n;i++) {
        		if(primes[i])
        			b.add(i);
        	}
        	
                 }
        
        
    }
    static int gcd(int a,int b){
        if(b==0)
        return a;
        return gcd(b,a%b);
    }
    static long GCD(long a,long b){
        if(b==0)
        return a;
        return GCD(b,a%b);
    }
    static long LCM(long a,long b) {
    	return (a*b)/GCD(a,b);
    }
    static int lcm(int a,int b) {
    	return (a*b)/gcd(a,b);
    }
    static ArrayList<Integer> segseive(int l,int r){
    	
    	ArrayList<Integer> isprime=new ArrayList<Integer>();
    	boolean p[]=new boolean[r-l+1];
    	Arrays.fill(p, true);
        
    	for(int i=0;b.get(i)*b.get(i)<=r;i++) {
    		int currprime=b.get(i);
    		int base=(l/currprime)*currprime;
    		if(base<l) {
    			base+=currprime;
    		}
    		for(int j=base;j<=r;j+=currprime) {
    			p[j-l]=false;
    		}
    		
    		
    		if(base==currprime) {
    			p[base-l]=true;
    		}
    		
    	}
    	for(int i=0;i<=r-l;i++) {
    		if(p[i])
    			isprime.add(i+l);
    	}
    	return isprime;
    }
      static int LowerBound(long a[], long x) { // x is the target value or key
  int l=-1,r=a.length;
  while(l+1<r) {
    int m=(l+r)>>>1;
    if(a[m]>=x) r=m;
    else l=m;
  }
  return r;
}
static int UpperBound(int a[], int x) {// x is the key or target value
    int l=-1,r=a.length;
    while(l+1<r) {
       int m=(l+r)>>>1;
       if(a[m]<=x) l=m;
       else r=m;
    }
    return l+1;
 }
 static void addEdge(ArrayList<ArrayList<Integer>> adj,int u,int v) {
	 adj.get(u).add(v);
	 adj.get(v).add(u);
 }
 static void BFS(ArrayList<ArrayList<Integer>> adj,int s,boolean visited[]) {
	 Queue<Integer> q=new LinkedList<>();
	 q.add(s);
	 visited[s]=true;
	 while(!q.isEmpty()) {
		 int u=q.poll();
		 for(int v:adj.get(u)) {
			 if(!visited[v]) {
				 visited[v]=!visited[v];
				 q.add(v);
			 }
		 }
	 }
 }
 static int BFSconnectedcount(ArrayList<ArrayList<Integer>> adj,int v) {
	 boolean visited[]=new boolean[v+1];
	 int count=0;
	 for(int i=0;i<v;i++) {
		 if(!visited[i]) {
			 BFS(adj,i,visited);
			 count++;
		 }
	 }
	 return count;
 }
 public static long power(long x, long y, long p) {
     long res = 1;
     x = x % p;
     while (y>0) {
        if ((y&1)==1) {
           res = (res*x) % p;
        }
        y = y >> 1;
        x = ( x * x ) % p;
     }
     return res;
  }
 public static long monInverse( long n, long p) {
     return power(n, p-2, p);
  }
  public static long nCrModPFermat( int n, int r, int p) {
     long[] fac = new long[n+1];
     fac[0] = 1;
     for (int i = 0; i < n; i++) {
        fac[i+1] = (fac[i]*(i+1))%p;
     }
long x = monInverse(fac[r], p);
long y = monInverse(fac[n-r], p);
//System.out.println(fac[n]);
     return (((fac[n]*x)% p) * ( y%p) ) % p;
  }
 

  // This class implements 
  // Comparator interface
 static class Point implements Comparable<Point> {
     
     int x;
     int y;
 
     public Point(int x, int y) {
         this.x = x;
         this.y = y;
     }
 
     
     @Override
     public int compareTo(Point o) {
        
				return x - o.x;
			
     }
    }
  static int maxSubArraySum(int a[], int size) 
  { 
  int max_so_far = a[0]; 
  int curr_max = a[0]; 

  for (int i = 1; i < size; i++) 
  { 
         curr_max = Math.max(a[i], curr_max+a[i]); 
      max_so_far = Math.max(max_so_far, curr_max); 
  } 
  return max_so_far; 
  } 
  static int maxsum(int a[],int n) {
	  int s=0;
	  int res=0;
	  int sum[]=new int[n];
	  sum[0]=a[0];
	  for(int i=1;i<n;i++) {
	     sum[i]=sum[i-1]+a[i];
	  }
	  for(int i=0;i<n;i++) {
		  s=Math.max(s, sum[i]);
	  }
	  return s;
  }
 static void leftRotate(int arr[], 
          int d, int n) 
{ 
for (int i = 0; i < d; i++) 
  leftRotatebyOne(arr, n); 
} 

static void leftRotatebyOne(int arr[], int n) 
{ 
int i, temp; 
temp = arr[0]; 
for (i = 0; i < n - 1; i++) 
  arr[i] = arr[i + 1]; 
arr[i] = temp; 
} 

static boolean checkleapyear(long n) {
	if(((n%4==0&&n%100!=0)||n%400==0)) {
		return true;
	}
	return false;
}
static void DFS(ArrayList<ArrayList<Integer>> adj,int v,int s ) {
	boolean visited[]=new boolean[v];
	DFSRec(adj,s,visited);
}
static void DFSRec(ArrayList<ArrayList<Integer>> adj,int s,boolean[] visited) {
	visited[s]=true;
	System.out.print(s+" ");
	for(int u:adj.get(s)) {
		if(!visited[u])
			DFSRec(adj,u,visited);
	}
}

    public static void main(String[] args) 
    { 
        FastReader sc=new FastReader(); 
        
        int t=1;
       //t=sc.nextInt();
       
        while(t-->0) {
        int n=sc.nextInt();
        
        int a[]=new int[n];
        ArrayList<Integer> l=new ArrayList<Integer>();
        StringBuilder sb=new StringBuilder();
        for(int i=0;i<n;i++) {
        	a[i]=sc.nextInt();
        	if(a[i]==0)
        		l.add(i);
        }
        int c=0;
        for(int i=0;i<n;i++) {
        	if(c+1<l.size()&&Math.abs(l.get(c)-i)>Math.abs(l.get(c+1)-i)) {
        		c++;
        	}
        	sb.append(Math.abs(l.get(c)-i)+" ");
        }
        System.out.println(sb);
        
        	}
        
    } 
    
}

