Please reason step by step, and put your final answer within \boxed{}.
If for a natural number $n$, the vertical addition $n + (n+1) + (n+2)$ does not produce any carry-over, then $n$ is called a "consecutive number." For example, 32 is a "consecutive number" because 32+33+34 does not produce any carry-over, while 23 is not a consecutive number because 23+24+25 produces a carry-over. How many "consecutive numbers" less than 200 are there?
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