Binary password

Zhomart uses binary string as a password for his computer. Now he forgot his old password and wants to get a new one, which is a binary string of length n. He believes that password is strong enough if it doesn't contain two consecutive zeroes. To get a new password he generates a random binary string of length n. If it is not strong he generates a random string again and so on until he finds a strong password. Find the expected number of random passwords Zhomart must generate before he finds strong one.


The only line of input contains one integer n (1n60).


Print the expected number as p / q, where p and q are relatively prime positive integers.

Time limit 1 second
Memory limit 128 MiB
Input example #1
Output example #1
Input example #2
Output example #2
Source 2014 KBTU Open, Spring Kazakhstan, Almaty, April 20, Problem A