Almost Automorphic Number

\[\Large 249^3 = 15438\underline{249}\]

An automorphic number is defined as a positive integer \(n\) such that the trailing digits of \(n^m\), where \(m\) is a positive integer, is \(n\) itself.

Let us define an almost automorphic number as a number where \(n\) only appears as the trailing digits of \(n^m\) when \(m\) is odd. How many almost automorphic numbers are less than 1000?

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