

'''simple docstring'''





from __future__ import annotations

import os
from collections.abc import Mapping

UpperCamelCase_							=					tuple[int, int]





class 		__SCREAMING_SNAKE_CASE       :







				def __init__(					self    :		Optional[int]		,				UpperCAmelCase__    :		set[int]		,				UpperCAmelCase__    :		Mapping[EdgeT, int]      ):
										'''simple docstring'''
										lowercase   :       set[int]								=vertices
										lowercase   :       dict[EdgeT, int]								={
										    (min(UpperCAmelCase__      ), max(UpperCAmelCase__      )): weight for edge, weight in edges.items()
										}







				def    lowerCamelCase_  (					self    :		Any		,				UpperCAmelCase__    :		EdgeT		,				UpperCAmelCase__    :		int      ):
										'''simple docstring'''
										self.vertices.add(edge[0]      )
										self.vertices.add(edge[1]      )
										lowercase   :       str								=weight







				def    lowerCamelCase_  (					self    :		List[Any]      ):
										'''simple docstring'''
										lowercase   :       Graph								=Graph({min(self.vertices      )}		,				{}      )
										lowercase   :       EdgeT
										lowercase   :       int
										lowercase   :       EdgeT
										lowercase   :       int

										while len(subgraph.vertices      ) < len(self.vertices      ):
																lowercase   :       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:
																																		lowercase   :       List[Any]								=edge
																																		lowercase   :       int								=weight

																subgraph.add_edge(UpperCAmelCase__		,				UpperCAmelCase__      )

										return subgraph






def 							_lowerCAmelCase (      __magic_name__	:    str = "p107_network.txt"	)							->     int:
						lowercase   :       str								=os.path.abspath(os.path.dirname(__magic_name__	)	)
						lowercase   :       str								=os.path.join(__magic_name__      ,   __magic_name__	)
						lowercase   :       dict[EdgeT, int]								={}
						lowercase   :       list[str]
						lowercase   :       int
						lowercase   :       int

						with open(__magic_name__	) as f:
												lowercase   :       Tuple								=f.read().strip().split('''\n'''	)

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

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

						lowercase   :       Graph								=Graph(set(range(len(__magic_name__	)	)	)      ,   __magic_name__	)

						lowercase   :       Graph								=graph.prims_algorithm()

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

						return initial_total - optimal_total


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








'''simple docstring'''





def 							_lowerCAmelCase (      __magic_name__	:    int      ,   __magic_name__	:    Optional[Any]	)							->     str:
						lowercase   :       Optional[Any]								=[0 for i in range(r + 1	)]
						# nc0 = 1
						lowercase   :       Optional[Any]								=1
						for i in range(1      ,   n + 1	):
												# to compute current row from previous row.
												lowercase   :       str								=min(__magic_name__      ,   __magic_name__	)
												while j > 0:
																		c[j] += c[j - 1]
																		j -= 1
						return c[r]







print(binomial_coefficient(n=10, r=5))





