Distances to Zero

Description:

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 ≤ a_i ≤ 10⁹).

Output:

Print the sequence d₀, d₁, ..., d_n - 1, where d_i is the difference of indices between i and nearest j such that a_j = 0. It is possible that i = j.

Sample Input:

9
2 1 0 3 0 0 3 2 4

Sample Output:

2 1 0 1 0 0 1 2 3 

Sample Input:

5
0 1 2 3 4

Sample Output:

0 1 2 3 4 

Sample Input:

7
5 6 0 1 -2 3 4

Sample Output:

2 1 0 1 2 3 4