Competitions

# DSA Week 1

# 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** (**0** ≤ **n** ≤ **2** * `10`

).^{9}

#### Output

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

Input example #1

99 268 6

Output example #1

2 4 0