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 $\leq 1000$

Input: n = 2-int
Output: 2-int
Explanation: A 2 × 2 board can be tiled either with two vertical dominoes or with two horizontal dominoes.

Input: n = 4-int
Output: 11-int
Explanation: There are 11 distinct tilings of a 2 × 4 board using dominoes and L-shaped trominoes (counting different placements and orientations as different tilings).

Input: n = 7-int
Output: 117-int
Explanation: As n grows, tromino placements create many additional configurations beyond domino-only tilings, and for n = 7 the total number of complete tilings is 117.

Input: n = 1000-int
Output: 979232805-int
Explanation: The number of tilings becomes extremely large, so the result is returned modulo 10^9 + 7.

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