You are given an integer n representing the number of nodes in a directed graph numbered from $0$ to $n - 1$, and a $2$D integer array edges where each edges[i] = $[u_i, v_i, w_i]$ denotes a directed edge from node $u_i$ to node $v_i$ with weight $w_i$.

You are also given a string labels of length n, where labels[i] is the character assigned to node $i$, and an integer k.

A path from node $0$ to node $n - 1$ is considered valid if the sequence of characters obtained by concatenating the labels of the nodes along the path contains at most k consecutive identical characters.

Return the minimum total weight of a valid path from node $0$ to node $n - 1$. If no such path exists, return $-1$.

Constraints:

• $1 \leq$ n $==$ labels.length $\leq 5 imes 10^4$

• $0 \leq$ edges.length $\leq 5 imes 10^4$

• edges[i] $== [u_i, v_i, w_i]$

• $0 \leq u_i, v_i \leq n - 1$

• $u_i \neq v_i$

• $1 \leq w_i \leq 10^4$

• labels consists of lowercase English letters.

• $1 \leq$ k $\leq 50$

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.