Same as Upside Down

\[ 1, 8, 11, 88, 101, 111, 181, 808, 818, 888, \ldots \]

The digits 0, 1 and 8 look the same when written upside down.
The 10th positive integer that looks the same when rotated \( 180^\circ \) and using only these digits is 888.

What is the 100th positive integer that looks the same when rotated \( 180^\circ \) and uses only these digits?

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