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. \InputFile One integer $n~(1 \le n \le 60)$. \OutputFile Print the expected number as $p / q$, where $p$ and $q$ are relatively prime positive integers.