





from __future__ import annotations

import os
from collections.abc import Mapping

__lowercase	: List[str]       =tuple[int, int]

class   A							:



      def __init__(						self:    Any		,	_lowerCAmelCase:    set[int]		,	_lowerCAmelCase:    Mapping[EdgeT, int]							)    ->     None:
         '''simple docstring'''

         UpperCAmelCase_           =vertices
         UpperCAmelCase_           ={
             (min(_lowerCAmelCase							), max(_lowerCAmelCase							)): weight for edge, weight in edges.items()
         }



      def 						lowerCAmelCase__     (						self:    int		,	_lowerCAmelCase:    EdgeT		,	_lowerCAmelCase:    int							)    ->     None:
         '''simple docstring'''

         self.vertices.add(edge[0]							)
         self.vertices.add(edge[1]							)
         UpperCAmelCase_           =weight






      def 						lowerCAmelCase__     (						self:    str							)    ->     Graph:
         '''simple docstring'''

         UpperCAmelCase_           =Graph({min(self.vertices							)}		,	{}							)
         UpperCAmelCase_           =42
         UpperCAmelCase_           =42
         UpperCAmelCase_           =42
         UpperCAmelCase_           =42

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

            subgraph.add_edge(_lowerCAmelCase		,	_lowerCAmelCase							)

         return subgraph




def      a__			(       lowercase__ = "p107_network.txt"	):






   '''simple docstring'''






   UpperCAmelCase_           =os.path.abspath(os.path.dirname(lowercase__	)	)
   UpperCAmelCase_           =os.path.join(lowercase__	,     lowercase__	)
   UpperCAmelCase_           ={}
   UpperCAmelCase_           =42
   UpperCAmelCase_           =42
   UpperCAmelCase_           =42

   with open(lowercase__	) as f:
      UpperCAmelCase_           =f.read().strip().split("\n"	)

   UpperCAmelCase_           =[line.split(","	) for line in data]

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

   UpperCAmelCase_           =Graph(set(range(len(lowercase__	)	)	)	,     lowercase__	)

   UpperCAmelCase_           =graph.prims_algorithm()

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

   return initial_total - optimal_total


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








def 		_A		(		_lowercase = 1_00 )					-> int:


     """simple docstring"""


     __UpperCamelCase =			0
     __UpperCamelCase =			0
     for i in range(1					,  n + 1 ):
          sum_of_squares += i**2
          sum_of_ints += i
     return sum_of_ints**2 - sum_of_squares


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


