Middle European Mathematical Olympiad 2019 Problem I-2

Let $n \geq 3$ be an integer. We say that a vertex $A_i$ ($1 \leq i \leq n$) of a convex polygon $A_1A_2\ldots A_n$ is Bohemian if its reflection with respect to the midpoint of the segment $A_{i-1}A_{i+1}$ (with $A_0 = A_n$ and $A_{n+1} = A_1$) lies inside or on the boundary of the polygon $A_1A_2\ldots A_n$. Determine the smallest possible number of Bohemian vertices a convex $n$-gon can have (depending on $n$).

(A convex polygon $A_1A_2\ldots A_n$ has $n$ vertices with all inner angles smaller than $180°$.)