2021 AMC 10A 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 , 200What is the median of the numbers in this list?

\textbf{(A)} ~100.5\qquad\textbf{(B)} ~134\qquad\textbf{(C)} ~142\qquad\textbf{(D)} ~150.5\qquad\textbf{(E)} ~167

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