Binary Operations Tables - II

Answer the following question based on the information given below.

Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables:

Thus, according to the first table f ⊕ g = a, while according to the second table g * h = f, and so on.

Also, let f² = f * f, g³= g * g * g, and so on.

What is the smallest positive integer n such that gⁿ = e?

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