You are given an integer array complexity of length n, where complexity[i] represents the security complexity of computer i. There are n computers numbered from $0$ to n $- 1$.

Initially, you have access to the root password to unlock computer $0$. A remaining computer j can be unlocked if and only if there is at least one already unlocked computer i such that complexity[i] < complexity[j].

An unlocking sequence is a permutation p of all computer indices from $0$ to n $- 1$ such that:

• p[0] $= 0$

• For every index k from $1$ to n $- 1$, there exists some index i with $0 \leq$ i $< k$ such that complexity[p[i]] < complexity[p[k]]

Return the number of valid unlocking permutations. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• $2 \leq$ complexity.length $\leq 10^5$

• $1 \leq$ complexity[i] $\leq 10^9$

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.