Power Strings

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: a0 = ‘’ (the empty string) and a(n+1) = a ∗ (an). Input Each test case is a line of input representing s, a string of printable characters. 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. Output For each s you should print the largest n such that s = an for some string a. Sample Input abcd aaaa ababab . Sample Output 1 4 3