Problem 22 (2025 AMC 8)

The Konigsberg School has assigned grades $1$ through $7$ to pods $A$ through $G$, one grade per pod. The school noticed that each pair of connected pods has been assigned grades differing by $2$ or more grade levels. (For example, grades $1$ and $2$ will not be in pods directly connected by a walkway.) What is the sum of the grade levels assigned to pods $C$, $E$, and $F$? [See figure in original PDF]