To transmit a positive integer less than 1000, the Networked Number Node offers two options.
Option 1: Pay $\$$d to send each digit d. Therefore, 123 would cost $\$$1 + $\$$2 + $\$$3 = $\$$6 to transmit.
Option 2: Encode the integer into binary (base 2) first, and then pay $\$$d to send each digit d. Therefore, 123 becomes 1111011 and would cost $\$$1 + $\$$1 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$1 = $\$$6.
What is the largest integer less than 1000 that costs the same whether using Option 1 or Option 2? Let's think step by step and output the final answer within \boxed{}.
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