Call a positive integer monotonous if it is a one-digit number or its digits, when read from left to right, form either a strictly increasing sequence (e.g., $23578$) or a strictly decreasing sequence (e.g., $987620$). However, a number is not considered monotonous if it contains the digit '5', unless it is the single-digit number $5$ itself. How many monotonous positive integers are there?