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 
#Name: Sofen Hoque Anonta
__metaclass__ = type
import math
import sys
import heapq

# take space seperated numbers (of specified type) as input and return them as a list


def input_array(convert_type):
    return [convert_type(x) for x in raw_input().split()]  # put seperator in split()

# ####################################################

def CF803B():

    n= input()
    a= input_array(int)

    dist = [300000] * n
    for i in xrange(n):
        if a[i] == 0 :
            dist[i]= 0
            for j in xrange(1, n-i):
                if a[i+j] == 0: break
                dist[i+j] = min(dist[i+j], j)

            for j in xrange(1, i+1):
                if a[i-j] == 0: break
                dist[i-j] = min(dist[i-j], j)

    for x in dist:
        print x,


CF803B()
