### Power Strings

Time Limit: 1000 ms Memory Limit: 65536 KiB

#### Problem Description

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).

#### 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 = a^n for some string a.

#### Sample Input

abcd
aaaa
ababab
.


#### Sample Output

1
4
3


#### Hint

This problem has huge input, use scanf instead of cin to avoid time limit exceed.