

'''simple docstring'''






from __future__ import annotations

import os
from collections.abc import Mapping

lowerCAmelCase__      		=			tuple[int, int]






class     lowercase_			:




  """simple docstring"""




  def __init__(   self     :  Optional[Any]      ,lowercase__     :  set[int]      ,lowercase__     :  Mapping[EdgeT, int]    ):
   __lowercase													=				vertices
   __lowercase													=				{
       (min(lowercase__    ), max(lowercase__    )): weight for edge, weight in edges.items()
   }






  def       SCREAMING_SNAKE_CASE   (   self     :  List[Any]      ,lowercase__     :  EdgeT      ,lowercase__     :  int    ):
   self.vertices.add(edge[0]    )
   self.vertices.add(edge[1]    )
   __lowercase													=				weight






  def       SCREAMING_SNAKE_CASE   (   self     :  Dict    ):
   __lowercase													=				Graph({min(self.vertices    )}      ,{}    )
   __lowercase													=				42
   __lowercase													=				42
   __lowercase													=				42
   __lowercase													=				42

   while len(subgraph.vertices    ) < len(self.vertices    ):
    __lowercase													=				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													=				edge
       __lowercase													=				weight

    subgraph.add_edge(lowercase__      ,lowercase__    )

   return subgraph


def 	_A  (					A__ = "p107_network.txt"   ):






 """simple docstring"""



 __lowercase													=				os.path.abspath(os.path.dirname(A__   )   )
 __lowercase													=				os.path.join(A__  ,       A__   )
 __lowercase													=				{}
 __lowercase													=				42
 __lowercase													=				42
 __lowercase													=				42

 with open(A__   ) as f:
  __lowercase													=				f.read().strip().split('''\n'''   )

 __lowercase													=				[line.split(''','''   ) for line in data]

 for edgea in range(1  ,       len(A__   )   ):
  for edgea in range(A__   ):
   if adjaceny_matrix[edgea][edgea] != "-":
    __lowercase													=				int(adjaceny_matrix[edgea][edgea]   )

 __lowercase													=				Graph(set(range(len(A__   )   )   )  ,       A__   )

 __lowercase													=				graph.prims_algorithm()

 __lowercase													=				sum(graph.edges.values()   )
 __lowercase													=				sum(subgraph.edges.values()   )

 return initial_total - optimal_total


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




'''simple docstring'''






def 	_A  (					A__ = 1000000   ):






 """simple docstring"""



 __lowercase													=				set(range(3  ,       A__  ,       2   )   )
 primes.add(2   )
 for p in range(3  ,       A__  ,       2   ):
  if p not in primes:
   continue
  primes.difference_update(set(range(p * p  ,       A__  ,       A__   )   )   )

 __lowercase													=				[float(A__   ) for n in range(limit + 1   )]

 for p in primes:
  for n in range(A__  ,       limit + 1  ,       A__   ):
   phi[n] *= 1 - 1 / p

 return int(sum(phi[2:]   )   )


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

