# Persistent Number

Very easy

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

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.

## Input

Each line contains one integer $n(0≤n≤2⋅10_{9})$.

## Output

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

## Examples

Input #1

Answer #1

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