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.

### Sample Input

abcd
aaaa
ababab
.

### Output for Sample Input

1
4
3