The first 2007 positive integers are each written in base 3.  How many of these base-3 representations are palindromes?  (A palindrome is a number that reads the same forward and backward.)
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The first 2007 positive integers are each written in base 3.  How many of these base-3 representations are palindromes?  (A palindrome is a number that reads the same forward and backward.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
100
The first 2007 positive integers are each written in base 3.  How many of these base-3 representations are palindromes?  (A palindrome is a number that reads the same forward and backward.)
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