Let $N$ be the number of ways of choosing a subset of $5$ distinct numbers from the set $$\{10a+b \mid 1 \leq a \leq 5, 1 \leq b \leq 5\}$$ where $a,b$ are integers, such that no two of the selected numbers have the same units digits and no two have the same tens digit. What is the remainder when $N$ is divided by $73$?

Let's think step by step and output the final answer within \boxed{}.
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