Shortest Repeating Unit

Statement

You are given a string s. Find the smallest length p such that p divides |s| and s is the first p characters repeated |s| / p times. If no shorter unit exists, the answer is |s|.

Input

One line: the string s.

Output

Print one integer: the smallest such length p.

Constraints

1 <= |s| <= 1000000
Only lowercase letters a to z.

Example 1

abcabcabc

3

The string is abc repeated three times.

Example 2

abcabcab

8

The string is not a whole number of repeats of anything shorter.