Question 6An integer is called *parity-monotonic* if its decimal representation $a_1 a_2 a_3 \ldots a_k$ satisfies $a_i \lt a_{i+1}$ if $a_i$ is odd, and $a_i \gt a_{i+1}$ if $a_i$ is even. How many four-digit parity-monotonic integers are there?