2020 AMC 12A Problem 10

There is a unique positive integer n such that\log_2{(\log_{16}{n})} = \log_4{(\log_4{n})}.What is the sum of the digits of n?

\textbf{(A) } 4 \qquad \textbf{(B) } 7 \qquad \textbf{(C) } 8 \qquad \textbf{(D) } 11 \qquad \textbf{(E) } 13

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.