Students, heights and their IQs

In the school morning assembly, $n$ students standing in a line. You, being the principal of the school know the heights and IQ levels of the students. This information is provided to you by an array $h$ and $iq$, where $h_i, iq_i$ denotes the height and the IQ of the $i$-th student, respectively. You want to find the longest subsequence of the students such that their heights are in strictly