from __future__ import annotations

import os
from collections.abc import Mapping

_lowercase							:      str      							=tuple[int, int]



class  SCREAMING_SNAKE_CASE_ :
		'''simple docstring'''


		def __init__(				self    :					Tuple      ,	SCREAMING_SNAKE_CASE__    :					set[int]      ,	SCREAMING_SNAKE_CASE__    :					Mapping[EdgeT, int]     )    ->				None:
									A						:     set[int]         =vertices
									A						:     dict[EdgeT, int]         ={
									    (min(SCREAMING_SNAKE_CASE__     ), max(SCREAMING_SNAKE_CASE__     )): weight for edge, weight in edges.items()
									}







		def 		SCREAMING_SNAKE_CASE_		(				self    :					Tuple      ,	SCREAMING_SNAKE_CASE__    :					EdgeT      ,	SCREAMING_SNAKE_CASE__    :					int     )    ->				None:
									self.vertices.add(edge[0]     )
									self.vertices.add(edge[1]     )
									A						:     Dict         =weight







		def 		SCREAMING_SNAKE_CASE_		(				self    :					Dict     )    ->				Graph:
									A						:     Graph         =Graph({min(self.vertices     )}      ,	{}     )
									A						:     EdgeT
									A						:     int
									A						:     EdgeT
									A						:     int

									while len(subgraph.vertices     ) < len(self.vertices     ):
																A						:     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:
																																					A						:     Dict         =edge
																																					A						:     str         =weight

																subgraph.add_edge(SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__     )

									return subgraph







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

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

							A						:     int         =[line.split(','					) for line in data]

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

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

							A						:     Graph         =graph.prims_algorithm()

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

							return initial_total - optimal_total


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







import math



def A__  (			lowercase:     int					)				->		list:
       A						:     Optional[Any]         =[True] * n
       A						:     Tuple         =False
       A						:     List[Any]         =False
       A						:     Dict         =True

       for i in range(3,		int(n**0.5 + 1					),		2					):
              A						:     Dict         =i * 2
              while index < n:
                     A						:     Dict         =False
                     A						:     Dict         =index + i

       A						:     Tuple         =[2]

       for i in range(3,		lowercase,		2					):
              if is_prime[i]:
                     primes.append(lowercase					)

       return primes



def A__  (			lowercase:     int = 999_966_663_333					)				->		int:
       A						:     Optional[int]         =math.floor(math.sqrt(lowercase					)					) + 100
       A						:     Optional[int]         =prime_sieve(lowercase					)

       A						:     Optional[Any]         =0
       A						:     List[Any]         =0
       A						:     Union[str, Any]         =primes[prime_index]

       while (last_prime**2) <= limit:
              A						:     Tuple         =primes[prime_index + 1]

              A						:     Optional[int]         =last_prime**2
              A						:     Tuple         =next_prime**2

              # Get numbers divisible by lps(current)
              A						:     int         =lower_bound + last_prime
              while upper_bound > current <= limit:
                     matches_sum += current
                     current += last_prime

              # Reset the upper_bound
              while (upper_bound - next_prime) > limit:
                     upper_bound -= next_prime

              # Add the numbers divisible by ups(current)
              A						:     List[Any]         =upper_bound - next_prime
              while current > lower_bound:
                     matches_sum += current
                     current -= next_prime

              # Remove the numbers divisible by both ups and lps
              A						:     Any         =0
              while upper_bound > current <= limit:
                     if current <= lower_bound:
                            # Increment the current number
                            current += last_prime * next_prime
                            continue

                     if current > limit:
                            break

                     # Remove twice since it was added by both ups and lps
                     matches_sum -= current * 2

                     # Increment the current number
                     current += last_prime * next_prime

              # Setup for next pair
              A						:     List[str]         =next_prime
              prime_index += 1

       return matches_sum


if __name__ == "__main__":
    print(solution())






