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 or a strictly decreasing sequence. For example, 3, 23578, and 987620 are monotonous, but 88, 7434, and 23557 are not. Find the total number of monotonous positive integers.

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