You are given an integer n representing the number of rows in a grid of size n $ imes$ $3$. You want to paint each cell of the grid using one of $3$ colors: Red, Yellow, or Green, such that no two adjacent cells share the same color. Two cells are considered adjacent if they share a common edge.

Return the total number of ways to paint the grid. Since the result can be very large, return it modulo $10^9 + 7$.

Constraints:

• n == grid.length

• $1 \leq$ n $\leq 5000$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

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.