Consider the set
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25 ... 123456789}
which consists of all positive integers whose digits strictly increase from left to right. This set is finite. What is the 100th smallest element of the set?
