Competitions

# KBTU OPEN 2014 Spring

# 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.

#### Input

The only line of input contains one integer **n** (**1** ≤ **n** ≤ **60**).

#### Ouput

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

Input example #1

1

Output example #1

1/1

Input example #2

4

Output example #2

2/1