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DNA can be represented as strings constructed from an alphabet of four characters: $\{$A$,$C$,$G$,$T$\}.$ We can thus construct

$4^(14)=268,435,456$ possible different DNA strings of length $14.$

If we were to construct a Multiway Trie $($MWT$)$ containing all $268,435,456$ possible DNA strings of length $14,$ what would be

the height of our MWT$?$

Note: Define the height of a tree to be the number of edges in the longest path from the root to a leaf.