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.*;

public class prob_803B {
	private static Scanner sc;
	private static int n;
	private static int[] a;
	private static List<Integer> l = new ArrayList<Integer>();
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		input();
		solve();
		output();
	}

	private static void output() {
		// TODO Auto-generated method stub
		for(int i=0; i<n; i++) {
			System.out.print(a[i] + " ");
		}
	}

	private static void solve() {
		// TODO Auto-generated method stub
		findList();
		
		for (int i=0; i<n; i++) {
			if (a[i] != 0 && a[i+1]==0) {
				a[i] = 1;
			} else if (a[i] == 0){
				a[i] = 0;
			} else {
				a[i] = miniDistance(i);
			}
			
		}
	}
	
	private static void findList() {
		// TODO Auto-generated method stub
		int head=0,tale = 0;
		boolean check = false;
		
		for (int i=0; i<n + 1; i++) {
			if (a[i] == 0 && check==false) {
				head = i;
				tale = i;
				check = true;
			} else if (a[i] == 0 && check == true) {
				tale += 1;
			} else if (check) {
				if (head == tale) {
					l.add(head);
				} else {
					l.add(head);
					l.add(tale);
				}
				check = false;
			} 
		}
	}

	private static int miniDistance(int i) {
		// TODO Auto-generated method stub
		int min = Integer.MAX_VALUE;
		
			for(Integer j:l) {
				int temp = i - j;
				if (temp < 0) {
					temp *= -1;
				}
				if (temp == 1) {
					return 1;
				}
				if (min > temp) {
					min = temp;
				}
			}
		
		
		return min;
	}

	private static void input() {
		// TODO Auto-generated method stub
		sc = new Scanner(System.in);
		
		n = sc.nextInt();
		a = new int[n+1];
		
		
		for(int i=0; i<n; i++) {
			a[i] = sc.nextInt();
			if (a[i] == 0) {
			}
		}
		a[n] = -1;
	}

}
