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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 $\overline{MAID}$ .