For an integer $$n\geq 3$$ and a permutation $$\sigma=(p_{1},p_{2},...,p_{n})$$ of $$\{1,2,...,n\}$$, we say $$p_{l}$$ is a landmark point if $$2\leq l\leq n-1$$ and $$(p_{l-1}-p_{l})(p_{l+1}-p_{l})>0$$. For example, for $$n=7$$ the permutation $$(2,7,6,4,5,1,3)$$ has four landmark points: $$p_{2}=7$$, $$p_{4}=4$$, $$p_{5}=5$$ and $$p_{6}=1$$. For a given $$n\geq 3$$, let $$L(n)$$ denote the number of permutations of $$\{1,2,...,n\}$$ with exactly one landmark point. Find the maximum $$n\geq 3$$ for which $$L(n)$$ is a perfect square.