You are tasked with building an ant colony consisting of $n$ rooms labeled from $0$ to $n - 1$. The construction dependencies are specified by an integer array prevRoom of length $n$, where prevRoom[i] represents the room that must be built before room i can be built.

Room $0$ is the starting point of the colony and has no prerequisite, indicated by prevRoom[0] being $-1$. For every other room i, you may only build room i after room prevRoom[i] has already been completed.

Return the number of distinct valid orders in which all $n$ rooms can be built. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• n $==$ prevRoom.length

• $2 \leq$ n $\leq 10^5$

• prevRoom[0] $== -1$

• $0 \leq$ prevRoom[i] $<$ n for all $1 \leq$ i $<$ n

• Every room is reachable from room $0$ once all the rooms are built.

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.