Recover a BST

The tests write a tree as a level-order list (row by row, left to right) with None for a missing child: [3, 9, 20, None, None, 15, 7] is a root 3 with children 9 and 20, where 20 has children 15 and 7. All trees in this topic that are called BSTs have different values.

Exactly two nodes of a BST had their values swapped by mistake. Put the values back so that the tree is a valid BST again, without changing the shape, and return the root.

For [3, 1, 4, None, None, 2] the answer is [2, 1, 4, None, None, 3].

Examples

Example 1

Input:

recover_tree(root)  # root = [1, 3, None, None, 2]

Output:

[3, 1, None, None, 2]

Example 2

Input:

recover_tree(root)  # root = [3, 1, 4, None, None, 2]

Output:

[2, 1, 4, None, None, 3]

Constraints

• 2 <= number of nodes <= 100000
• The tree is not deeper than 800 levels.
• Exactly two values were swapped.