Alice and Bob have an undirected graph containing n nodes labeled from $1$ to n. You are given an integer n and a $2 ext{D}$ array edges, where edges[i] $= [type_i, u_i, v_i]$ represents a bidirectional edge between nodes $u_i$ and $v_i$.

The parameter $type_i$ defines the accessibility of the edge:

• Type $1$: Traversable only by Alice.

• Type $2$: Traversable only by Bob.

• Type $3$: Traversable by both Alice and Bob.

A graph is fully traversable by an individual if that person can reach every node from every other node using only their accessible edges.

Return the maximum number of edges you can remove such that the graph remains fully traversable by both Alice and Bob. If it is impossible for both Alice and Bob to fully traverse the graph, return $-1$.

Constraints:

• $1 \leq$ n $\leq 10^5$

• $1 \leq$ edges.length $\leq \min(10^5, 3 \cdot$ n $\cdot ($ n $- 1) / 2)$

• edges[i].length $= 3$

• $1 \leq type_i \leq 3$

• $1 \leq u_i < v_i \leq$ n

• All tuples $(type_i, u_i, v_i)$ are distinct.

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.