AMC 10 2021a Problem 16

In the following list of numbers, the integer $n$ appears $n$ times in the list for $1 \leq n \leq 200$.$$1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \ldots, 200, 200, \ldots , 200$$What is the median of the numbers in this list? $\textbf{(A)} ~100.5 \textbf{(B)} ~134 \textbf{(C)} ~142 \textbf{(D)} ~150.5 \textbf{(E)} ~167$