As an experiment the Educational Codeforces Round 33 will be rated for Div. 2. ×

B. Distances to Zero
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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