A digit string is considered good if the digits at even indices (starting from index $0$) are even ($0$, $2$, $4$, $6$, or $8$) and the digits at odd indices are prime ($2$, $3$, $5$, or $7$).

Given an integer n, return the total number of good digit strings of length n. Since the answer may be large, return it modulo $10^9 + 7$.

Note: A digit string may contain leading zeros, and indices are numbered starting from $0$ from left to right.

Constraints:

• $1 \leq$ n $\leq 10^{15}$

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.