Height of Binary Tree After Subtree Removal Queries

You are given the `root` of a **binary tree** with `n` nodes. Each node is assigned a unique value from `1` to `n`. You are also given an array `queries` of size `m`. You have to perform `m` **independent** queries on the tree where in the `ith` query you do the following: - **Remove** the subtree rooted at the node with the value `queries[i]` from the tree. It is **guaranteed** that `queries[i]` will **not** be equal to the value of the root. Return _an array _`answer`_ of size _`m`_ where _`answer[i]`_ is the height of the tree after performing the _`ith`_ query_. **Note**: - The queries are independent, so the tree returns to its **initial** state after each query. - The height of a tree is the **number of edges in the longest simple path** from the root to some node in the tree.   **Example 1:** **Input:** root = [1,3,4,2,null,6,5,null,null,null,null,null,7], queries = [4] **Output:** [2] **Explanation:** The diagram above shows the tree after removing the subtree rooted at node with value 4. The height of the tree is 2 (The path 1 -> 3 -> 2). ``` **Example 2:** **Input:** root = [5,8,9,2,1,3,7,4,6], queries = [3,2,4,8] **Output:** [3,2,3,2] **Explanation:** We have the following queries: - Removing the subtree rooted at node with value 3. The height of the tree becomes 3 (The path 5 -> 8 -> 2 -> 4). - Removing the subtree rooted at node with value 2. The height of the tree becomes 2 (The path 5 -> 8 -> 1). - Removing the subtree rooted at node with value 4. The height of the tree becomes 3 (The path 5 -> 8 -> 2 -> 6). - Removing the subtree rooted at node with value 8. The height of the tree becomes 2 (The path 5 -> 9 -> 3). ```   **Constraints:** - The number of nodes in the tree is `n`. - `2 <= n <= 105` - `1 <= Node.val <= n` - All the values in the tree are **unique**. - `m == queries.length` - `1 <= m <= min(n, 104)` - `1 <= queries[i] <= n` - `queries[i] != root.val`