Given an integer n, return the number of distinct ways to completely tile a $2 imes n$ board using $2 imes 1$ dominoes and L shaped trominoes. Since the answer can be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n $\leq 1000$

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We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.