Competitions

# Persistent Number

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 find its persistence.

#### Input

Each line contains one integer n (0n2 * 109).

#### Output

For each number n print on a separate line its persistence.

Time limit 1 second
Memory limit 128 MiB
Input example #1
99
268
6

Output example #1
2
4
0