You are given a directed acyclic graph (DAG) with $n$ nodes, labeled from $0$ to $n - 1$. The graph is represented as an adjacency list, where graph[i] is a list of all nodes to which node i has a directed edge to.

Your task is to find all possible paths from node $0$ (the source) to node $n - 1$ (the target) and return them as a list of paths. Each path should be represented as a list of node indexes.

Note: You may return the answer in any order.

Constraints:

• $2 \leq$ $n$ $\leq 15$

• $0 \leq$ graph[i][j] $<$ $n$

• All nodes in graph[i] are unique.

• The graph is guaranteed to be a DAG (no cycles).

• There are no self-loops (i.e., graph[i] does not contain i).

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 on how to solve this problem.

Implement your solution in the following coding playground.