A farmer's rectangular field is partitioned into a $2\times 2$ grid of $4$ rectangular sections as shown in the figure. In each section the farmer will plant one crop: Pears, Quinces, Raspberries, or Strawberries. The farmer does not want to grow Pears and Quinces in any two sections that share a border. The farmer also does not want to grow Quinces and Raspberries in any two sections that share a border. Furthermore, the farmer does not want to grow Raspberries and Strawberries 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?