# Fibonacci Divisibility Graph

Let $$\{F_i\}_{i=1}^\infty$$ be the sequence of Fibonacci numbers; that is, $$F_1 = F_2 = 1$$ and $$F_{n+2} = F_{n+1} + F_n$$ for all $$n \ge 1$$.

Consider a graph with vertices labeled $$F_3, F_4, F_5, \ldots, F_N$$, and two (different) vertices $$x,y$$ are connected by an edge if and only if $$x|y$$ or $$y|x$$. The above picture is the graph for $$N = 12$$.

Find the largest $$N$$ such that this graph is planar. If there is no largest $$N$$, enter $$0$$.

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