A derangement is defined as a permutation of an array such that no element appears in its original position.

Given an integer n representing an array initially containing n distinct elements from $1$ to n, return the total number of derangements of the array.

Since the answer may be large, return the result modulo $10^9 + 7$.

Constraints:

• $1 \leq `n` \leq 10^6$

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.