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B. Distances to Zero

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given the array of integer numbers *a*_{0}, *a*_{1}, ..., *a*_{n - 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* ≤ 2·10^{5}) — length of the array *a*. The second line contains integer elements of the array separated by single spaces ( - 10^{9} ≤ *a*_{i} ≤ 10^{9}).

Output

Print the sequence *d*_{0}, *d*_{1}, ..., *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*.

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

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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