AMC 10 2020a Problem 17

Define $$P(x) =(x-1^2)(x-2^2)\cdots(x-100^2).$$ How many integers $n$ are there such that $P(n)\leq 0$? $\textbf{(A) } 4900 \textbf{(B) } 4950 \textbf{(C) } 5000 \textbf{(D) } 5050 \textbf{(E) } 5100$