You are given an integer n representing a complete binary tree containing $2^n - 1$ nodes. The root node is labeled $1$, and each node with value val has a left child labeled $2 imes ext{val}$ and a right child labeled $2 imes ext{val} + 1$.

You are also given a $2$D integer array queries of size m, where queries[i] $= [a_i, b_i]$. For each query, an undirected edge is added between node $a_i$ and node $b_i$, creating a cycle.

Return an integer array ans of length m, where ans[i] is the number of nodes in the cycle formed during the $i^{ ext{th}}$ query.

Note: Queries are processed independently. The edge added in a query is removed before moving to the next query.

Constraints:

• $2 \leq$ n $\leq 30$

• m $==$ queries.length

• $1 \leq$ m $\leq 10^5$

• queries[i].length $== 2$

• $1 \leq a_i, b_i \leq 2^n - 1$

• $a_i \neq b_i$

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.