AMC 10 2021-fall-a Problem 18

A farmer's rectangular field is partitioned into $2$ by $2$ grid of $4$ rectangular sections as shown in the figure. In each section the farmer will plant one crop: corn, wheat, soybeans, or potatoes. The farmer does not want to grow corn and wheat in any two sections that share a border, and the farmer does not want to grow soybeans and potatoes in any two sections that share a border. Given these restrictions, in how many ways can the farmer choose crops to plant in each of the four sections of the field?

$\textbf{(A)}\ 12 \textbf{(B)}\ 64 \textbf{(C)}\ 84 \textbf{(D)}\ 90 \textbf{(E)}\ 144$