Count Perfect Wake Numbers ≤ N (Digit DP)

Count Perfect Wake Numbers in [1, N] A positive integer is called a Perfect Wake Number iff it satisfies all of the following: Its decimal representation does not contain digit 0. No digits are repeated. No digit is adjacent to two strictly larger digits. Formally, for digit array d[1..L], it is not allowed to have an index i with 1 < i < L such that d[i-1] > d[i] and d[i+1] > d[i]. Given an integer N (1 ≤ N ≤ 10^18), return how many integers in [1, N] are Perfect Wake Numbers. Examples 196, 23, and 12463 are Perfect Wake Numbers. 1546 is not (digit 4 has neighbors 5 and 6, both larger). 320 is not (contains 0). 34321 is not (repeats digit 3). Example Input 1 Output 1