





from __future__ import annotations

import os
from collections.abc import Mapping

lowerCAmelCase_        =							tuple[int, int]



class    __lowerCAmelCase			:






			def __init__(self   ,				__magic_name__   ,				__magic_name__       )	->  None:


							'''simple docstring'''



							snake_case_		:       set[int]           =    vertices
							snake_case_		:       dict[EdgeT, int]           =    {
							    (min(__magic_name__       ), max(__magic_name__       )): weight for edge, weight in edges.items()
							}






			def      lowerCamelCase    (self   ,				__magic_name__   ,				__magic_name__       )	->  None:


							'''simple docstring'''



							self.vertices.add(edge[0]       )
							self.vertices.add(edge[1]       )
							snake_case_		:       List[str]           =    weight






			def      lowerCamelCase    (self       )	->  Graph:


							'''simple docstring'''



							snake_case_		:       Graph           =    Graph({min(self.vertices       )}   ,				{}       )
							snake_case_		:       EdgeT
							snake_case_		:       int
							snake_case_		:       EdgeT
							snake_case_		:       int

							while len(subgraph.vertices       ) < len(self.vertices       ):
											snake_case_		:       List[Any]           =    max(self.edges.values()       ) + 1
											for edge, weight in self.edges.items():
															if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
																			if weight < min_weight:
																							snake_case_		:       Union[str, Any]           =    edge
																							snake_case_		:       Dict           =    weight

											subgraph.add_edge(__magic_name__   ,				__magic_name__       )

							return subgraph






def 	lowerCamelCase_		(							_UpperCamelCase = "p107_network.txt"					)						->		int:






				"""simple docstring"""


				snake_case_		:       str           =    os.path.abspath(os.path.dirname(_UpperCamelCase					)					)
				snake_case_		:       str           =    os.path.join(_UpperCamelCase					,							_UpperCamelCase					)
				snake_case_		:       dict[EdgeT, int]           =    {}
				snake_case_		:       list[str]
				snake_case_		:       int
				snake_case_		:       int

				with open(_UpperCamelCase					) as f:
								snake_case_		:       int           =    f.read().strip().split('''\n'''					)

				snake_case_		:       Union[str, Any]           =    [line.split(''','''					) for line in data]

				for edgea in range(1					,							len(_UpperCamelCase					)					):
								for edgea in range(_UpperCamelCase					):
												if adjaceny_matrix[edgea][edgea] != "-":
																snake_case_		:       Tuple           =    int(adjaceny_matrix[edgea][edgea]					)

				snake_case_		:       Graph           =    Graph(set(range(len(_UpperCamelCase					)					)					)					,							_UpperCamelCase					)

				snake_case_		:       Graph           =    graph.prims_algorithm()

				snake_case_		:       int           =    sum(graph.edges.values()					)
				snake_case_		:       int           =    sum(subgraph.edges.values()					)

				return initial_total - optimal_total


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




UpperCAmelCase   :    Any     =		[0, 2, 4, 6, 8]
UpperCAmelCase   :    Optional[Any]     =		[1, 3, 5, 7, 9]






def 	__lowerCamelCase						(							lowerCamelCase__		:						int  ,							lowerCamelCase__		:						int  ,							lowerCamelCase__		:						list[int]  ,							lowerCamelCase__		:						int      ):





			'''simple docstring'''




			if remaining_length == 0:
						if digits[0] == 0 or digits[-1] == 0:
									return 0

						for i in range(length // 2 - 1  ,							-1  ,							-1      ):
									remainder += digits[i] + digits[length - i - 1]

									if remainder % 2 == 0:
												return 0

									remainder //= 10

						return 1

			if remaining_length == 1:
						if remainder % 2 == 0:
									return 0

						lowerCamelCase    		=  0
						for digit in range(10      ):
									lowerCamelCase    		=  digit
									result += reversible_numbers(
									    0  ,							(remainder + 2 * digit) // 10  ,							lowerCamelCase__  ,							lowerCamelCase__      )
						return result

			lowerCamelCase    		=  0
			for digita in range(10      ):
						lowerCamelCase    		=  digita

						if (remainder + digita) % 2 == 0:
									lowerCamelCase    		=  ODD_DIGITS
						else:
									lowerCamelCase    		=  EVEN_DIGITS

						for digita in other_parity_digits:
									lowerCamelCase    		=  digita
									result += reversible_numbers(
									    remaining_length - 2  ,							(remainder + digita + digita) // 10  ,							lowerCamelCase__  ,							lowerCamelCase__  ,							)
			return result






def 	__lowerCamelCase						(							lowerCamelCase__		:						int = 9      ):





			'''simple docstring'''




			lowerCamelCase    		=  0
			for length in range(1  ,							max_power + 1      ):
						result += reversible_numbers(lowerCamelCase__  ,							0  ,							[0] * length  ,							lowerCamelCase__      )
			return result


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

