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 . 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 . 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.
One integer .
Print the expected number as , where and are relatively prime positive integers.