You are given an integer n. You have an infinite supply of coins with values $1$, $2$, and $6$, and at most two coins of value $4$.

Return the total number of distinct combinations of coins that sum up to n. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n $\leq 10^5$

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.