Time Limit: 1000 mSec Memory Limit : 32768 KB

Given two strings *a* and *b* we define *a*b* to be
their concatenation. For example, if *a = "abc"* and *b = "def"*
then *a*b = "abcdef"*. If we think of concatenation as multiplication,
exponentiation by a non-negative integer is defined in the normal way:
*a^0 = ""* (the empty string) and *a^(n+1) = a*(a^n)*.

Each test case is a line of input
representing *s*, a string of printable characters.
For each *s* you should print the largest *n* such that
*s = a^n* for some string *a*. The length of *s* will
be at least 1 and
will not exceed 1 million characters. A line containing a period follows the
last test case.

abcd
aaaa
ababab
.

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