AMC 8 2020 Problem 21

A game board consists of $64$ squares that alternate in color between black and white. The figure below shows square $P$ in the bottom row and square $Q$ in the top row. A marker is placed at $P.$ A step consists of moving the marker onto one of the adjoining white squares in the row above. How many $7$-step paths are there from $P$ to $Q?$ (The figure shows a sample path.)

$\textbf{(A) }28 \textbf{(B) }30 \textbf{(C) }32 \textbf{(D) }33 \textbf{(E) }35$