Problem 16 (2021 AMC 12A)

In the following list of numbers, the integer $n$ appears $n$ times in the list for $1 \leq n \leq 200$: $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \dots, 200, \dots, 200$. What is the median of the numbers in this list?