You are given an integer array nums sorted in ascending order. Your task is to construct a height-balanced binary search tree (BST) from it and return its root.

Note: A height-balanced binary search tree, also known as a Balanced BST, is a type of binary search tree where, for every node, the heights of the left and right subtrees differ by no more than one.

Example 1:

Input: nums = [-7, -2, 0, 6, 8]
Output: [0, -7, 6, null, -2, null, 8] 
Explanation: Traversal Order (Pre-order DFS): 0 → -7 → -2 → 6 → 8
        0
       / \
    -7     6
      \     \
      -2     8
Since there are multiple ways to choose the middle element for balance (when the subarray length is even), here are other valid BST outputs:
[
  [0, -2, 6, -7, null, null, 8],
  [0, -7, 8, null, -2, 6],
  [0, -2, 8, -7, null, 6]
]

Example 2:

Input: nums = [2, 3, 4, 7]
Output: [3, 2, 4, null, null, null, 7]

Explanation: Pre-order Traversal (DFS): visit root → left → right
          3
       /     \
     2         4
    / \      /   \
 null null null    7
                  / \
               null null
There are multiple valid balanced BSTs for this input array:
  Option 1: Root = 3 => [3, 2, 4, null, null, null, 7],
  Option 2: Root = 4 => [4, 3, 7, 2] or [4, 2, 7, null, 3]

Example 3:

Input: nums = [5]
Output: [5]
Explanation: The array has one value, so the only possible BST contains one node.

Constraints

1 <= nums.length <= 10⁴
-10⁴ <= nums[i] <= 10⁴

nums is sorted in a strictly increasing order.

39. Convert Sorted Array to Balanced BST