You are given an integer n representing the number of nodes in a directed graph labeled from $0$ to $n - 1$, and a $2 {D}$ integer array edges where edges[i] $= [u_i, v_i, start_i, end_i]$.

Each entry in edges indicates a directed edge from node $u_i$ to node $v_i$ that can only be traversed if you depart from node $u_i$ at a time $t$ such that $start_i \leq t \leq end_i$. Traversing any edge takes exactly $1$ unit of time.

You start at node $0$ at time $t = 0$. You are allowed to wait at any node for any non negative amount of time.

Return the minimum time required to reach node $n - 1$. If it is impossible to reach node $n - 1$, return $-1$.

Constraints:

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ edges.length $\leq 10^5$

• edges[i] $= [u_i, v_i, start_i, end_i]$

• $0 \leq u_i, v_i \leq n - 1$

• $u_i \neq v_i$

• $0 \leq start_i \leq end_i \leq 10^9$

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.