294. He's Circles

time limit per test: 1.75 sec.
memory limit per test: 65536 KB
input: standard
output: standard



He wrote n letters "X" and "E" in a circle. He thought that there were 2n possibilities to do it, because each letter may be either "X" or "E". But Qc noticed that some different sequences of letters can be transformed one to another with a circular shift (thus representing actually the same circular string).
For example, strings "XXE"-"XEX"-"EXX" are actually the same.
Qc wants to know how many different circular strings of n letters exist. Help him to find that out.

Input
The input file contains a single integer 1 <= n <= 200000.

Output
Output a single integer --- the number circular strings of length n.

Sample test(s)

Input
Test #1 
3 
 
Test #2 
4 
 

Output
Test #1 
4 
 
Test #2 
6 
  
  
Author:Anton Golubev, Petrazavodsk SU 
Resource:Anton Golubev (Hedgehog)'s Contest #2 from Annual Summer Russian Teams Meeting in Petrozavodsk State University 
Date:August 26, 2005