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 sys

n = int(sys.stdin.readline())

a = sys.stdin.readline().strip().split()

def findDistancesToZero(n,a):
    pos_zero_left = a.index('0')
    pos_zero_right = a.index('0')
    pos = 0
    positions = ''
    while pos<n:
        worked = False
        while pos<=pos_zero_right:            
            print(str(min(abs(pos-pos_zero_left),abs(pos-pos_zero_right))),end=' ')
            pos+=1
            worked = True
        pos_zero_left = pos_zero_right
        try:
            pos_zero_right = a.index('0',pos)            
        except:
            pos_zero_right = pos_zero_left
            False
        if worked:
            pos-=1
        if pos_zero_left == pos_zero_right:            
            pos+=1
            while pos<n:
                print(str(abs(pos-pos_zero_left)),end=' ')
                pos+=1
            pos-=1
        pos+=1    
    return positions

findDistancesToZero(n,a)
