# Nikhil the Ant

In a regular tetrahedron labeled $$ABCD$$, Nikhil the ant sits at vertex $$A$$. After every minute, he travels to one of the other three vertices with equal probability. Given that the probability that after $$7$$ minutes Nikhil is at vertex $$A$$ is $$\frac{m}{729}$$, find $$m$$.

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