Persistent Number

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 $99,9\cdot 9=81,8\cdot 1=8$. Thus, the persistence of $99$ is $2$. You will be given $n$, and you must find its persistence.

Input

Each line contains one integer $n(0\le n\le 2\cdot 10^9)$.

Output

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

Examples