MathNet 2021 — Part 02 Question 60

Suppose that $A = \{1, 2, 3\}$, $B = \{2x + y \mid x, y \in A, x \lt y\}$, $C = \{2x + y \mid x, y \in A, x \gt y\}$. Then the sum of all the elements of $B \cap C$ is ______.