

'''simple docstring'''






from __future__ import annotations

from typing import Any






class     lowercase_			:




		"""simple docstring"""




		def __init__(   self     :  List[str]      ,lowercase__     :  Optional[Any]    ):
			__lowercase													=				num_of_nodes
			__lowercase													=				[]
			__lowercase													=				{}






		def       SCREAMING_SNAKE_CASE   (   self     :  Optional[Any]      ,lowercase__     :  List[str]      ,lowercase__     :  int      ,lowercase__     :  Optional[Any]    ):
			self.m_edges.append([u_node, v_node, weight]    )






		def       SCREAMING_SNAKE_CASE   (   self     :  Dict      ,lowercase__     :  Optional[Any]    ):




			if self.m_component[u_node] == u_node:
				return u_node
			return self.find_component(self.m_component[u_node]    )






		def       SCREAMING_SNAKE_CASE   (   self     :  Tuple      ,lowercase__     :  Any    ):




			if self.m_component[u_node] != u_node:
				for k in self.m_component:
					__lowercase													=				self.find_component(A_    )






		def       SCREAMING_SNAKE_CASE   (   self     :  Optional[int]      ,lowercase__     :  Optional[Any]      ,lowercase__     :  List[str]      ,lowercase__     :  List[str]    ):




			if component_size[u_node] <= component_size[v_node]:
				__lowercase													=				v_node
				component_size[v_node] += component_size[u_node]
				self.set_component(A_    )

			elif component_size[u_node] >= component_size[v_node]:
				__lowercase													=				self.find_component(A_    )
				component_size[u_node] += component_size[v_node]
				self.set_component(A_    )






		def       SCREAMING_SNAKE_CASE   (   self     :  Any    ):
			__lowercase													=				[]
			__lowercase													=				0

			__lowercase													=				[-1] * self.m_num_of_nodes

			# A list of components (initialized to all of the nodes)
			for node in range(self.m_num_of_nodes    ):
				self.m_component.update({node: node}    )
				component_size.append(1    )

			__lowercase													=				self.m_num_of_nodes

			while num_of_components > 1:
				for edge in self.m_edges:
					__lowercase													=				edge

					__lowercase													=				self.m_component[u]
					__lowercase													=				self.m_component[v]

					if u_component != v_component:

						for component in (u_component, v_component):
							if (
							    minimum_weight_edge[component] == -1
							    or minimum_weight_edge[component][2] > w
							):
								__lowercase													=				[u, v, w]

				for edge in minimum_weight_edge:
					if isinstance(A_      ,A_    ):
						__lowercase													=				edge

						__lowercase													=				self.m_component[u]
						__lowercase													=				self.m_component[v]

						if u_component != v_component:
							mst_weight += w
							self.union(A_      ,A_      ,A_    )
							print(F"Added edge [{u} - {v}]\nAdded weight: {w}\n"    )
							num_of_components -= 1

				__lowercase													=				[-1] * self.m_num_of_nodes
			print(F"The total weight of the minimal spanning tree is: {mst_weight}"    )


def 	_A  (					):






	"""simple docstring"""



	pass


if __name__ == "__main__":
	import doctest

	doctest.testmod()




'''simple docstring'''






def 	_A  (					A__ = 50   ):






 """simple docstring"""



 __lowercase													=				[1] * (length + 1)

 for row_length in range(3  ,       length + 1   ):
  for block_length in range(3  ,       row_length + 1   ):
   for block_start in range(row_length - block_length   ):
    ways_number[row_length] += ways_number[
        row_length - block_start - block_length - 1
    ]

   ways_number[row_length] += 1

 return ways_number[length]


if __name__ == "__main__":
 print(f'{solution() = }')

