Given a non-negative integer n, repeatedly multiply together all of its digits to form a new number, and repeat this process until the result is a single digit (0-9). Count how many such multiplication rounds are needed; this count is the multiplicative persistence of n.
For example, 39 -> 39=27 -> 27=14 -> 1*4=4 (3 rounds). If n is already a single digit, the persistence is 0.
Input format
Line 1: n given as a string of decimal digits (no leading zeros unless n is exactly 0), with at most 20 digits.
Output format
A single integer: the multiplicative persistence of n.
Constraints
nhas between 1 and 20 digitsncontains only characters0-9, with no leading zero unlessnis exactly0