Count Good Nodes Along Root Paths

A node in a binary tree is considered **good** if, on the path from the root down to that node, no ancestor has a strictly greater value than the node's own value.

Given the root of a binary tree, return the total number of good nodes.

**Example 1:**
```
Input: root = [5, 3, 8, 3, 4, 7, 9]
Output: 5
```
Explanation: Nodes 5 (root, always good), 8, 3 (right child, equal to parent), 4, 9 are good. Node 3 (left child of 5) and 7 are also good — trace the max along each path.

**Example 2:**
```
Input: root = [10, 5, 15, 3, 7, null, 20]
Output: 4
```
Explanation: Nodes 10, 15, 20, and 7 are good. Node 5 is not (parent is 10). Node 3 is not (ancestor 10 exists).