A 3-ary tree is a rooted tree where each parent has at most three children, and each child is labeled with 1, 2, or 3 (and siblings all have different labels). A full 3-ary tree is a 3-ary tree where each parent has exactly 3 children. Two 3-ary trees are isomorphic as 3-ary trees if they are isomorphic as rooted trees and the isomorphism preserves the labels of the children. Show that there is a a bijection between the set of nonisomorphic (as 3-ary trees) 3-ary trees with n vertices and the set of nonisomorphic (as 3-ary trees) full 3-ary trees with 2n + 1 terminal vertices.

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