Count Perfect Wake Numbers up to N

Fresh coding round 1: define a Perfect Wake Number as a positive integer with all distinct digits, no `0`, and no digit adjacent to two strictly-larger digits. Given `n`, count how many Perfect Wake Numbers lie in `[1, n]`. The base check is easy; the count follow-up is the actual signal. Requirements A positive integer is a Perfect Wake Number iff all of the following hold: No two digits in its decimal representation are equal. No digit is 0. No interior digit is strictly less than both of its left and right neighbors. (Equivalently, no digit is adjacent to two strictly larger digits — so the digit sequence has no "strict valley".) Part 1 (warm-up): implement isPerfect(x). Part 2 (the actual question): given n, return how many integers in [1, n] are Perfect Wake Numbers. Examples 196 → perfect (digits 1,9,6 all distinct, no 0, 9 is not a valley) 23 → perfect 12463 → perfect (1<2, 2<4, 4>6? No, 4<6, 6>3 — 6 is not a valley because its right neighbor 3 is smaller) 1546 → not perfect (4 is adjacent to 5 and 6, both strictly larger) 320 → not perfect (contains 0) 34321 → not perfect (digit 3 repeats) Notes Part 1 is a linear scan; Part 2 is digit DP with state (position, mask of used digits, last digit, is_tight against n). Track whether the previous step went up or down to detect a future valley. Multiple candidates report not finishing Part 2 in the 45-minute window. The interviewer is generally patient and dispenses hints ("think DP" / "think digit DP") when you stall. Watch out: the "no valley" rule is about interior digits, so the first and last digit are never themselves the valley; they can still create one for their neighbor. The full prompt is short and recent — expect the follow-up to vary (e.g. count exactly-K-digit Perfect Wake Numbers). Preparation Drill digit DP templates: classic digit-DP problems — "count digit one", "non-negative integers without consecutive ones", "numbers at most N given digit set", "numbers with repeated digits" — cover "count integers ≤ n satisfying digit predicate." Practice bitmask-over-digits + tight-flag state machines. Memorize the standard skeleton: recurse over positions, accept any digit ≤ n's digit when tight, else any digit 1..9.