cyclicString

We call a string cyclic if it can be obtained by concatenating another string to itself many times (for example, s2 = "abcabcabcabc..." is cyclic since it can be obtained from s1 = "abc" in such a way).

You’re given a substring s of some cyclic string. What’s the length of the smallest possible string that can be concatenated to itself many times to obtain this cyclic string?

Example

For s = "cabca", the output should be cyclicString(s) = 3.

"cabca" is a substring of a cycle string "abcabcabcabc..." that can be obtained by concatenating "abc" to itself. Thus, the answer is 3.

Input/Output

• [execution time limit] 0.5 seconds 

• [input] string s

  Guaranteed constraints:
  2 ≤ s.length ≤ 1000.

• [output] integer