$$$\qquad$$$There are $$$N$$$ planets in Adams' Universe, numbered from $$$1$$$ to $$$N$$$. Planets are connected with $$$N - 1$$$ space lifts. $$$i$$$-th space lift $$$(1 \leq i \leq N - 1)$$$ connects planet $$$A_i$$$ to planet $$$B_i$$$. Each space lift can move in any direction. You can travel from one planet to any other planet using space lifts.

$$$\qquad$$$Presently, Adams' Universe is divided into $$$K$$$ galaxies, numbered from $$$1$$$ to $$$K$$$. Planet $$$j (1 \leq j \leq N)$$$ belongs to the galaxy $$$C_j$$$. Every galaxy contains at least one planet.

$$$\qquad$$$One galaxy will be chosen as the main transportation hub (MTH) by Chief Coordinator Beeblebrox. For national security reasons, MTH must satisfy the following conditions.

$$$\qquad$$$You should be able to travel from any planet of MTH to any other planet of MTH, visiting only planets which belong to MTH.

$$$\qquad$$$Nevertheless, Chief Coordinator Beeblebrox noticed that it might be the case that no galaxy of Adams' Universe satisfies the condition, and he is not able to choose the MTH. $$$\qquad$$$In order to solve this problem, Chief Coordinator Beeblebrox can merge galaxies. Precisely, he can do the following operation.

$$$\qquad$$$Choose $$$x$$$ and $$$y$$$ satisfying $$$(1 \leq x, y \leq K)$$$ and $$$x \neq y$$$ and change the galaxies of planets belonging to the galaxy $$$y$$$ so that every planet belonging to the galaxy $$$y$$$ becomes a planet belonging to the galaxy $$$x$$$.

$$$\qquad$$$Merging galaxies is very labor-intensive, so Chief Coordinator Beeblebrox would like to minimize the number of times to merge galaxies in order to choose MTH.

$$$\qquad$$$Since Beeblebrox coordinates the whole Adams' Universe, which is not simple, he will not be able to do it himself, so he decided to ask you for help. Calculate the minimum number of times to merge galaxies to choose MTH.