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Problem C
Digits

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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 x0, define a sequence using the following recurrence:

xi+1=the number of digits in the decimalrepresentation of xi

Your task is to determine the smallest positive i such that xi=xi1.

Input

Input consists of several lines. Each line contains a value of x0. Every value of x0 is non-negative and has no more than one million digits. The last line of input contains the word END. There are at most 10000 values of x0 and the size of the input file is at most 2 MB.

Output

For each value of x0, output the corresponding value of i.

Sample Input 1 Sample Output 1
42
5
END
3
2
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