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 math,string,itertools,collections,re,fractions,array,copy
import bisect
import heapq
from itertools import chain, dropwhile, permutations, combinations
from collections import deque, defaultdict, OrderedDict, namedtuple, Counter, ChainMap


# Guide:
#   1. construct complex data types while reading (e.g. graph adj list)
#   2. avoid any non-necessary time/memory usage
#   3. avoid templates and write more from scratch
#   4. switch to "flat" implementations

def VI(): return list(map(int,input().split()))
def I(): return int(input())
def LIST(n,m=None): return [0]*n if m is None else [[0]*m for i in range(n)]
def ELIST(n): return [[] for i in range(n)]
def MI(n=None,m=None): # input matrix of integers
    if n is None: n,m = VI()
    arr = LIST(n)
    for i in range(n): arr[i] = VI()
    return arr
def MS(n=None,m=None): # input matrix of strings
    if n is None: n,m = VI()
    arr = LIST(n)
    for i in range(n): arr[i] = input()
    return arr
def MIT(n=None,m=None): # input transposed matrix/array of integers
    if n is None: n,m = VI()
    a = MI(n,m)
    arr = LIST(m,n)
    for i,l in enumerate(a):
        for j,x in enumerate(l):
            arr[j][i] = x
    return arr

def main(info=0):
    n = I()
    a = VI()
    z = [i for i in range(n) if a[i]==0]
    i=0
    j=0
    x = [j for j in range(z[0], -1, -1)]
    # print(z)
    for i in range(1, len(z)):
        d = z[i]-z[i-1]
        x += [j for j in range(1, d//2)]
        if d%2 == 1 and d>2: x += [d//2, ]
        x += [j for j in range(d//2, -1, -1)]
    x += [j for j in range(1, n-z[-1])]
    print(" ".join(str(j) for j in x))



if __name__ == "__main__":
    main()
