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.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;

public class B {
	
	public static void main(String[] args){
		try(final Scanner sc = new Scanner(System.in)){
			final int n = sc.nextInt();
			
			long[] array = new long[n];
			for(int i = 0; i < n; i++){
				array[i] = sc.nextLong();
			}
			
			int[] from_left  = new int[n];
			int[] from_right = new int[n];
			
			for(int i = 0, left = Integer.MAX_VALUE / 2; i < n; i++){
				if(array[i] == 0){ 
					left = 0;
				}else{ 
					left++;
				}
				
				from_left[i] = left;
			}
			
			for(int i = n - 1, right = Integer.MAX_VALUE / 2; i >= 0; i--){
				if(array[i] == 0){
					right = 0;
				}else{
					right++;
				}
				
				from_right[i] = right;
			}
			
			for(int i = 0; i < n; i++){
				System.out.print((i == 0 ? "" : " ") + Math.min(from_left[i], from_right[i]));
			}
			System.out.println();
		}
		
	}
	
	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;

		public Scanner(InputStream is) {
			br = new BufferedReader(new InputStreamReader(is));
		}

		private void getLine() {
			try {
				while (!hasNext()) {
					tok = new StringTokenizer(br.readLine());
				}
			} catch (IOException e) { /* ignore */
			}
		}

		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}

		public String next() {
			getLine();
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public void close() {
			try {
				br.close();
			} catch (IOException e) { /* ignore */
			}
		}
	}
}
