CF1349A Orac and LCM

For the multiset of positive integers $ s=\{s_1,s_2,\dots,s_k\} $ , define the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of $ s $ as follow: - $ \gcd(s) $ is the maximum positive integer $ x $ , such that all integers in $ s $ are divisible on $ x $ . - $ \textrm{lcm}(s) $ is the minimum positive integer $ x $ , that divisible on all integers from $ s $ . For example, $ \gcd(\{8,12\})=4,\gcd(\{12,18,6\})=6 $ and $ \textrm{lcm}(\{4,6\})=12 $ . Note that for any positive integer $ x $ , $ \gcd(\{x\})=\textrm{lcm}(\{x\})=x $ . Orac has a sequence $ a $ with length $ n $ . He come up with the multiset $ t=\{\textrm{lcm}(\{a_i,a_j\})\ |\ i

The first line contains one integer $ n\ (2\le n\le 100\,000) $ . The second line contains $ n $ integers, $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 200\,000 $ ).

Print one integer: $ \gcd(\{\textrm{lcm}(\{a_i,a_j\})\ |\ i

For the first example, $ t=\{\textrm{lcm}(\{1,1\})\}=\{1\} $ , so $ \gcd(t)=1 $ . For the second example, $ t=\{120,40,80,120,240,80\} $ , and it's not hard to see that $ \gcd(t)=40 $ .