Digits

A googol written out in decimal has $101$ digits. A googolplex has one plus a googol digits. That’s a lot of digits!

Given any number $x_{0}$, define a sequence using the following recurrence:

\[ x_{i+1} = \text {the number of digits in the decimal representation of }x_{i} \]Your task is to determine the smallest positive $i$ such that $x_{i} = x_{i-1}$.

Input consists of several lines. Each line contains a value
of $x_{0}$. Every value of
$x_{0}$ is non-negative
and has no more than one million digits. The last line of input
contains the word `END`. There are at
most $10\, 000$ values of
$x_0$ and the size of the
input file is at most $2$
MB.

For each value of $x_0$, output the corresponding value of $i$.

Sample Input 1 | Sample Output 1 |
---|---|

42 5 END |
3 2 |