B"Mars is home to an unusual species of spiders -- Binary spiders. Right now, Martian scientists are observing a colony of n spiders, the i -th of which has a_i legs. Some of the spiders are friends with each other. Namely, the i -th and j -th spiders are friends if gcd(a_i, a_j) ne 1 , i. e., there is some integer k ge 2 such that a_i and a_j are simultaneously divided by k without a remainder. Here gcd(x, y) denotes the greatest common divisor (GCD) of integers x and y . Scientists have discovered that spiders can send messages. If two spiders are friends, then they can transmit a message directly in one second. Otherwise, the spider must pass the message to his friend, who in turn must pass the message to his friend, and so on until the message reaches the recipient. Let's look at an example. Suppose a spider with eight legs wants to send a message to a spider with 15 legs. He can't do it directly, because gcd(8, 15) = 1 . But he can send a message through the spider with six legs because gcd(8, 6) = 2 and gcd(6, 15) = 3 . Thus, the message will arrive in two seconds. Right now, scientists are observing how the s -th spider wants to send a message to the t -th spider. The researchers have a hypothesis that spiders always transmit messages optimally. For this reason, scientists would need a program that could calculate the minimum time to send a message and also deduce one of the optimal routes. The first line of input contains an integer n ( 2 <= n <= 3 cdot10^5 ) -- the number of spiders in the colony. The second line of input contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 3 cdot10^5 ) -- the number of legs the spiders have. The third line of input contains two integers s and t ( 1 <= s, t <= n ) --the spiders between which the message must be sent. If it is impossible to transmi"...