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.lang.Math;
import java.math.BigInteger;

public class Problem {

	public static void main(String[] args) throws IOException {

		new Problem().run();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok;
	static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	Problem() throws FileNotFoundException{

		if (ONLINE_JUDGE) {
			in = new BufferedReader(new InputStreamReader(System.in)); 
            out = new PrintWriter(System.out); 
		} else {
			in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter("output.txt");
		}
		tok = new StringTokenizer("");
	}

	// ======================================================

	int INF = Integer.MAX_VALUE;
	List<Integer>[] graph;
	boolean[] used;
	int[] def;
	void solve() throws IOException {
		int n = rI();
		int[] arr = new int[n];
		int[] distances = new int[n];
		boolean[] used = new boolean[n];
		Queue<Integer> q = new ArrayDeque<>();
		for(int i=0;i<n;++i){
			arr[i]=rI();
			if(arr[i]==0){
				q.add(i);
				used[i] = true;
			}
		}
		while(q.size()>0){
			int cur = q.poll();
			if(cur<n-1&&!used[cur+1]){
				q.add(cur+1);
				used[cur+1] = true;
				distances[cur+1] = distances[cur]+1;
			}
			if(cur>0&&!used[cur-1]){
				q.add(cur-1);
				used[cur-1] = true;
				distances[cur-1] = distances[cur]+1;
			}
		}
		for(int i: distances){
			out.print(i+" ");
		}
	}
	
	// ======================================================
	void run() throws IOException {
		solve();
		out.close();
	}


	double sqrt(double m){
		double l = 0;
		double r = 1000000000+9;
		int i=1000;
		while(r-l>6){
			double mid = (r+l)/2;
			if(mid*mid>m){
				r = mid;
			}else{
				l=mid;
			}
			--i;
		}
		return l;
	}
	int countPow(int m,int n){
		int ans = 0;
		while(m%n==0&&m>0){
			ans++;
			m/=n;
		}
		return ans;
	}
	long binPow(long a, long b){
		if(b == 0){
			return 1;
		}
		if(b%2==1){
			return a*binPow(a,b-1);
		}else{
			long c = binPow(a,b/2);
			return c*c;
		}
		
	}
	long gcd(long a, long b){
		return b==0?a:gcd(b,a%b);
	}
	
	long pow(long x, long k){
		long ans=1;
		for(int i=0;i<k;++i){
			ans*=x;
		}
		return ans;
	}
	//////////////////////////////////////////////////////////////////////


	String delimiter = " ";
	String readLine() throws IOException {
		return in.readLine();
	}
	String rS() throws IOException {
		while (!tok.hasMoreTokens()) {
			String nextLine = readLine();
			if (null == nextLine)
				return null;

			tok = new StringTokenizer(nextLine);
		}

		return tok.nextToken(delimiter);
	}
	int rI() throws IOException {
		return Integer.parseInt(rS());
	}

	long rL() throws IOException {
		return Long.parseLong(rS());
	}
	int[] rA(int b) {
		int a[] = new int[b];
		for (int i = 0; i < b; i++) {
			try {
				a[i] = rI();
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return a;
	}
	
	int[] readSortedIntArray(int size) throws IOException {
	        Integer[] array = new Integer[size];

	        for (int index = 0; index < size; ++index) {
	            array[index] = rI();
	        }
	        Arrays.sort(array);

	        int[] sortedArray = new int[size];
	        for (int index = 0; index < size; ++index) {
	            sortedArray[index] = array[index];
	        }

	        return sortedArray;
	    }

}