You are given the array of integer numbers a₀, a₁, ..., 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.

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).

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.