A $4\times 4\times 4$ open cubical box contains 64 identical small cubes that exactly fill the box. How many of these small cubes touch the bottom or one of the four lateral sides of the box?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A $4\times 4\times 4$ open cubical box contains 64 identical small cubes that exactly fill the box. How many of these small cubes touch the bottom or one of the four lateral sides of the box?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
52
A $4\times 4\times 4$ open cubical box contains 64 identical small cubes that exactly fill the box. How many of these small cubes touch the bottom or one of the four lateral sides of the box?
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