# Calling All Powers That Give Two Digits

Let $$A,B,C$$ and $$D$$ be distinct single digit positive integers such that: $A^B =\overline{CD} \text{ and } A+B=C+D$

Compute $$\overline{AB} + \overline{BC} + \overline{CD} + \overline{DA}$$.

Clarification: $$\overline{AB}$$ denotes a 2-digit integer with $$A$$ and $$B$$ as its digits.

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