Record Setters on the Trail

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Trail markers on a mountain are arranged as a binary tree rooted at base camp, each marker stamped with an altitude. Hikers always walk from the root downward. A marker earns a record plaque if no marker on the path from base camp to it is stamped higher than it — ties still count as a record.

Given the root of a binary tree, return how many nodes are records: nodes whose value is greater than or equal to every value on the path from the root down to them. The root is always a record.

Tests pass a level-order array; implement the core in _count_good on real nodes.

Example 1

in values = [3, 1, 4, 3, null, 1, 5]

out 4

Records: the root 3, the 4, the 5, and the deep 3 (path 3 → 1 → 3 never exceeds 3).

Example 2

in values = [3, 3, null, 4, 2]

out 3

Root 3, the left 3 (tie counts), and the 4. The 2 is below a 3.

Example 3

in values = [1]

out 1

Constraints

· 1 <= number of nodes <= 10^5
· -10^4 <= node value <= 10^4