SRM 343 Div 2

Given a number x, we can define p(x) as the product of the digits of x. We can then form a sequence x, p(x), p(p(x))... The persistence of x is then defined as the index (0-based) of the first single digit number in the sequence. For example, using 99, we get the sequence 99, 9*9 = 81, 8*1 = 8. Thus, the persistence of 99 is 2. You will be given n, and you must return its persistence.