Digits

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description



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 decimal representation of xi

Your task is to determine the smallest positive i such that xi = xi-1.

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.

Output

For each value of x0 given in the input, output one line containing the smallest positive i such that xi = xi-1.

Sample Input

42 END

Sample Output

3

Hint

chenrui

Source

University of Waterloo Local Contest 2009.0

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