HMMT November 2019 T10

A convex 2019-gon $A_{1} A_{2} \ldots A_{2019}$ is cut into smaller pieces along its 2019 diagonals of the form $A_{i} A_{i+3}$ for $1 \leq i \leq 2019$, where $A_{2020}=A_{1}, A_{2021}=A_{2}$, and $A_{2022}=A_{3}$. What is the least possible number of resulting pieces?