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 $\leq 3 \times 10^4$

• $0 \leq$ ...