
from __future__ import annotations

import os
from collections.abc import Mapping

lowercase__							:							Union[str, Any]									=			tuple[int, int]






class        SCREAMING_SNAKE_CASE__    :

							"""simple docstring"""






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





													'''simple docstring'''






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



							def     A__		(  self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_			)->   None:





													'''simple docstring'''






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



							def     A__		(  self			)->   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(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_			)

													return subgraph





def 	A_ (							snake_case							:   str = "p107_network.txt" )      ->    int:



						'''simple docstring'''

						__UpperCamelCase       =			os.path.abspath(os.path.dirname(snake_case ) )
						__UpperCamelCase       =			os.path.join(snake_case ,      snake_case )
						__UpperCamelCase       =			{}
						__UpperCamelCase       =			42
						__UpperCamelCase       =			42
						__UpperCamelCase       =			42

						with open(snake_case ) as f:
												__UpperCamelCase       =			f.read().strip().split('''\n''' )

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

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

						__UpperCamelCase       =			Graph(set(range(len(snake_case ) ) ) ,      snake_case )

						__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() = }")






from collections import Counter
from timeit import timeit




def 	A_ (							snake_case							:   str = "" ,      )      ->    bool:



						'''simple docstring'''

						return sum(c % 2 for c in Counter(input_str.replace(''' ''' ,      '''''' ).lower() ).values() ) < 2




def 	A_ (							snake_case							:   str = "" )      ->    bool:



						'''simple docstring'''

						if len(snake_case ) == 0:
												return True
						__UpperCamelCase       =			input_str.replace(''' ''' ,      '''''' ).lower()
						# character_freq_dict: Stores the frequency of every character in the input string
						__UpperCamelCase       =			{}

						for character in lower_case_input_str:
												__UpperCamelCase       =			character_freq_dict.get(snake_case ,      0 ) + 1
						__UpperCamelCase       =			0

						for character_count in character_freq_dict.values():
												if character_count % 2:
																		odd_char += 1
						if odd_char > 1:
												return False
						return True




def 	A_ (							snake_case							:   str = "" )      ->    None:



						'''simple docstring'''

						print('''\nFor string = ''' ,      snake_case ,      ''':''' )
						print(
						    '''> can_string_be_rearranged_as_palindrome_counter()''' ,      '''\tans =''' ,      can_string_be_rearranged_as_palindrome_counter(snake_case ) ,      '''\ttime =''' ,      timeit(
						        '''z.can_string_be_rearranged_as_palindrome_counter(z.check_str)''' ,      setup='''import __main__ as z''' ,      ) ,      '''seconds''' ,      )
						print(
						    '''> can_string_be_rearranged_as_palindrome()''' ,      '''\tans =''' ,      can_string_be_rearranged_as_palindrome(snake_case ) ,      '''\ttime =''' ,      timeit(
						        '''z.can_string_be_rearranged_as_palindrome(z.check_str)''' ,      setup='''import __main__ as z''' ,      ) ,      '''seconds''' ,      )


if __name__ == "__main__":
				lowercase__							:							Tuple									=			input(
				    "Enter string to determine if it can be rearranged as a palindrome or not: "
				).strip()
				benchmark(check_str)
				lowercase__							:							Dict									=			can_string_be_rearranged_as_palindrome_counter(check_str)
				print(F"{check_str} can {'' if status else 'not '}be rearranged as a palindrome")




