You 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