Magic Array

Sonya loves problems with sequences, so she has a large collection of different sequences at home. Some of these sequences are magic sequences. A *magic sequence* with length $N$ is an integer sequence $s_1, s_2, \ldots, s_N$ with the following properties: - At least one of its elements is $0$. - For each valid $i$, $s_i$ is the distance of element $s_i$ to the closest zero element. Formally,