Problem C
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:

Your task is to determine the smallest positive $i$ such that $x_{i} = x_{i-1}$.

Input

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.

Output

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

42
5
END

3
2