You are given an undirected, unrooted tree with n nodes indexed from $0$ to $n - 1$. The tree structure is defined by a $2$D integer array edges of length $n - 1$, where edges[i] = [a_i, b_i] indicates an undirected edge between nodes a_i and b_i. You are also given a binary array coins of size n, where coins[i] is either $0$ or $1$, and a value of $1$ means node i contains a coin.

You may begin at any node in the tree and repeatedly perform the following operations in any order:

• Collect all coins located at a distance of at most $2$ from your current node, or

• Move to any directly adjacent node in the tree.

Return the minimum number of edges you must traverse to collect every coin and return to your starting node.

Note: If the same edge is traversed multiple times, each traversal counts separately toward the total.

Constraints:

• n == coins.length

• $1 \leq$ n $\leq 3 \times 10^4$

• $0 \leq$ coins[i] $\leq 1$

• edges.length == n - 1

• edges[i].length == 2

• $0 \leq$ a_i, b_i $<$ n

• a_i != b_i

• edges represents a valid tree.

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.