You are given an integer n representing the number of nodes in a directed graph, labeled from $0$ to $n - 1$. You are also given a $2 {D}$ integer array edges, where edges[i] = [u_i, v_i, w_i] represents a directed edge from node u_i to node v_i with a traversal cost of w_i.

You can traverse any directed edge from u_i to v_i with cost w_i. Additionally, you may reverse any edge and traverse it in the opposite direction from v_i to u_i with a cost of $2 \times w_i$.

Return the minimum total cost to travel from node $0$ to node $n - 1$. If node $n - 1$ cannot be reached, return $-1$.

Constraints:

• $2 \leq$ n $\leq 5 \times 10^4$

• $1 \leq$ edges.length $\leq 10^5$

• edges[i] $= [u_i, v_i, w_i]$

• $0 \leq u_i, v_i \leq n - 1$

• $1 \leq w_i \leq 1000$

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.