Given a number x, we define a function 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 find its persistence.
Each line contains one integer n(0≤n≤2⋅109).
For each number n print on a separate line its persistence.