A convex $2019$-gon $A_1A_2\ldots A_{2019}$ is divided into smaller pieces by cutting along its $2019$ diagonals of the form $A_iA_{i+3}$ for $1 \le i \le 2019$, where $A_{2020} = A_1$, $A_{2021} = A_2$, and $A_{2022} = A_3$. What is the least possible number of resulting pieces?

Let's think step by step and output the final answer within \boxed{}.
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