For any positive integer $$n$$, the Farey sequence $$F_n$$ is the set of irreducible rational numbers $$\dfrac{a}{b}$$ with $$0\leq a\leq b\leq n$$ and $$\mathrm{gcd}(a,b)=1$$ arranged in increasing order. The first three Farey sequences are: $\begin{array}{lcl} F_1 & = & \displaystyle{\left\{\frac{0}{1},\frac{1}{1}\right \}} \\ F_2 & = & \displaystyle{\left\{\frac{0}{1},\frac{1}{2},\frac{1}{1}\right \}} \\ F_3 & = & \displaystyle{\left\{\frac{0}{1},\frac{1}{3},\frac{1}{2},\frac{2}{3},\frac{1}{1}\right \}} \end{array}$
Compute the maximum value of $$n$$ for which the number of terms of $$F_n$$ does not exceed $$500$$.