Distances to Zero

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Description

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.

Sample Input

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 

Sample Output

None

Hint

None

Source

None

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