Brilli the Ant is Brilliant! Part 2

Brilli the ant, is on the 3-dimensional plane. He is standing on \( (0,0,0) \) . It takes him \( 2 \) minutes to crawl one unit. The probability that Brilli is crawls to \( (2,2,2) \) can be written as \( \frac{m}{n} \). Find \( m+n \)

Notes and Assumptions: Brilli only moves forwards and backwards, left and right, and Brilli also moves up and down.

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