In a three-digit number, the hundreds digit is greater than 5, the tens digit is greater than 4 but less than 8, and the units digit is the smallest prime number. How many three-digit numbers satisfy all of these conditions?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In a three-digit number, the hundreds digit is greater than 5, the tens digit is greater than 4 but less than 8, and the units digit is the smallest prime number. How many three-digit numbers satisfy all of these conditions?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
In a three-digit number, the hundreds digit is greater than 5, the tens digit is greater than 4 but less than 8, and the units digit is the smallest prime number. How many three-digit numbers satisfy all of these conditions?
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