Define a $k$-periodic string as follows:

A string $s$ is $k$-periodic if the length of the string $|s|$ is a multiple of $k$, and if you chop the string up into $|s|/k$ substrings of length $k$, then each of those substrings (except the first) is the same as the previous substring, but with its last character moved to the front.

For example, the following string is $3$-periodic:abccabbcaabc

The above string can break up into substrings abc, cab, bca, and abc, and each substring (except the first) is a right-rotation of the previous substring (abc -> cab -> bca -> abc)

Given a string, determine the smallest k for which the string is k-periodic.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The single line of input contains a string $s$ ($1 \le |s| \le 100$) consisting only of lowercase letters.

-----Output-----
Output the integer $k$, which is the smallest $k$ for which the input string is $k$-periodic.

-----Examples-----
Sample Input 1:
aaaaaaaa
Sample Output 1:
1

Sample Input 2:
abbaabbaabba
Sample Output 2:
2

Sample Input 3:
abcdef
Sample Output 3:
6

见题面

见题面