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Number Theory Level pending

Let \(O,D,A,I,M,O \) be distinct digits such that \(O^3 \) is equal to the 3-digit integer \(\overline{DAD} \), and the square of the 2-digit integer, \(\overline{IM} ^2 \) is equal to the 3-digit integer \(\overline{MOM} \). Find the value of the 4-digit integer \(\overline{MAID} \).

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