Erdős Problem #862 — Number of Maximal Sidon Sets

Let $A_1(N)$ be the number of inclusion-maximal Sidon subsets of $\{1,\ldots,N\}$, where a set is Sidon if $a+b=c+d$ for elements of the set implies that the two unordered pairs $\{a,b\}$ and $\{c,d\}$ are equal. Is it true that

$$\log_2 A_1(N)=o\!\left(N^{1/2}\right)\qquad(N\to\infty)?$$