Given the root of a binary search tree (BST), construct and return a balanced BST containing the same node values. If multiple valid solutions exist, return any one of them.

A BST is considered balanced if the height difference between the left and right subtrees of every node is at most one.

Height of a node is the number of edges in the longest path from that node down to a leaf. For balance checking, an empty subtree has height -1.

Example 1:

Input: root = [5, 3, null, -2, null, -6]
Output: [-2, -6, 3, null, null, null, 5]
Explanation: 
The original tree is a valid but unbalanced BST. 
One valid balanced BST places `-2` as the root, `-6` as its left child, and `3` as its right child with `5` as the right child of `3`.

Other valid balanced BST outputs include:
[3,-2,5,-6], [-2,-6,5,null,null,3], [3,-6,5,null,-2]

Example 2:

Input: root = [2,1,3]
Output: [2,1,3]

Example 3:

Input: root = [10]
Output: [10]
Explanation: A single-node BST is already balanced.

Constraints

The number of nodes in the tree is in the range [1, 10⁴].
-10⁵<= Node.val <= 10⁵
All node values are unique.

81. Convert BST to Balanced BST