Almost Automorphic Number

2493=15438249\Large 249^3 = 15438\underline{249}

An automorphic number is defined as a positive integer nn such that the trailing digits of nmn^m, where mm is a positive integer, is nn itself for all m>0m>0.

Let us define an almost automorphic number as a number where nn only appears as the trailing digits of nmn^m for all odd m>0m>0. How many almost automorphic numbers are less than 1000?

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