ZS the Coder and Chris the Baboon has explored Udayland for quite some time. They realize that it consists of n towns numbered from 1 to n.

There are n directed roads in the Udayland. i-th of them goes from town i to some other town a_i (a_i ≠ i). ZS the Coder can flip the direction of any road in Udayland, i.e. if it goes from town A

ZS the Coder considers the roads in the Udayland confusing, if there is a sequence of distinct towns A₁, A₂, ..., A_k (k > 1) such that for every 1 ≤ i < k there is a road from town A_i to town A_i + 1 and another road from town A

Now ZS the Coder wonders how many sets of roads (there are 2ⁿ variants) in initial configuration can he choose to flip such that after flipping each road in the set exactly once, the resulting network will not

Note that it is allowed that after the flipping there are more than one directed road from some town and possibly some towns with no roads leading out of it, or multiple roads between any pair of cities.