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.math.*;
import java.io.*;

public class Main {
	static int n,pos;
	static int left[];
	static int right[];
	static int arr[];

	public static void main(String[] args) throws IOException {
		Reader in = new Reader();
		PrintWriter out = new PrintWriter(System.out);
		n = in.nextInt();
		arr = new int[n];
		left = new int[n];
		right = new int[n];
		for(int i = 0; i < n; i++) {
			arr[i] = in.nextInt();
			if(arr[i] == 0) {
				left[i] = right[i] = 0;
			}
		}
		pos = -1;
		for(int i = 0; i < n; i++) {
			if(arr[i] == 0) {
				pos = i;
			} else {
				if(pos != -1) {
					left[i] = i - pos;
				} else {
					left[i] = Integer.MAX_VALUE;
				}
			}
		}
		pos = -1;
		for(int i = n-1; i >= 0; i--) {
			if(arr[i] == 0) {
				pos = i;
			} else {
				if(pos != -1) {
					right[i] = pos - i;
				} else {
					right[i] = Integer.MAX_VALUE;
				}
			}
		}
		for(int i = 0; i < n; i++) {
			out.print(Math.min(left[i],right[i]) + " ");
		}
		out.println();
		out.close();
	}

	static class Pair<X extends Comparable<X>,Y extends Comparable<Y>> implements Comparable<Pair<X,Y>> {
		X x;
		Y y;

		public Pair(X a,Y b) {
			x = a;
			y = b;
		}

		@Override
		@SuppressWarnings("unchecked")
		public boolean equals(Object p) {
			if(!(p instanceof Pair)) return false;
			return compareTo((Pair<X,Y>) p) == 0;
		}

		@Override
		public int compareTo(Pair<X,Y> p) {
			int xres = p.x.compareTo(x), yres = p.y.compareTo(y);
			if(xres == 0 && yres == 0) {
				return 0;
			} else if(xres >= 0) {
				if(xres > 0) {
					return -1;
				} else {
					return (yres > 0) ? -1 : 1;
				}
			} else {
				return 1;
			}
		}

		@Override
		public int hashCode() {
			return Objects.hash(x,y);
		}

		@Override
		public String toString() {
			return "(" + x + "," + y + ")";
		}
	}

	// Fast input class
	static class Reader
	{
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader()
		{
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException
		{
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String next() throws IOException
		{
			byte[] buf = new byte[10000]; // line length
			int cnt = 0, c;
			Boolean white;
			while ((c = read()) != -1)
			{
				white = Character.isWhitespace(c);
				if (white && cnt > 0)
					break;
				if(!white) {
					buf[cnt++] = (byte) c;
				}
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException
		{
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
			{
				ret = ret * 10 + c - '0';
			}  while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException
		{
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			}
			while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException
		{
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			}
			while ((c = read()) >= '0' && c <= '9');

			if (c == '.')
			{
				while ((c = read()) >= '0' && c <= '9')
				{
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException
		{
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException
		{
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException
		{
			if (din == null)
				return;
			din.close();
		}
	}
}
