AMC 12 2007b Problem 21

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.)

$\mathrm {(A)} 100 \mathrm {(B)} 101 \mathrm {(C)} 102 \mathrm {(D)} 103 \mathrm {(E)} 104$