
import numpy as np

lowerCamelCase_						: Optional[int]         =  [
    ["""a""", """b""", """c""", """d""", """e"""],
    ["""f""", """g""", """h""", """i""", """k"""],
    ["""l""", """m""", """n""", """o""", """p"""],
    ["""q""", """r""", """s""", """t""", """u"""],
    ["""v""", """w""", """x""", """y""", """z"""],
]

class        _UpperCamelCase				:






			'''simple docstring'''

			def __init__(       self :       Optional[int]      ):
							UpperCamelCase_:							Any	=						np.array(snake_case_      )

			def       lowerCAmelCase__	(       self :       Optional[Any]						,	snake_case_ :       Optional[Any]      ):
							UpperCamelCase_:							Optional[Any]	=						np.where(letter == self.SQUARE      )
							UpperCamelCase_:							List[str]	=						np.concatenate([indexa + 1, indexa + 1]      )
							return indexes

			def       lowerCAmelCase__	(       self :       Dict						,	snake_case_ :       List[str]						,	snake_case_ :       List[Any]      ):
							UpperCamelCase_:							int	=						self.SQUARE[indexa - 1, indexa - 1]
							return letter

			def       lowerCAmelCase__	(       self :       Optional[Any]						,	snake_case_ :       List[Any]      ):
							UpperCamelCase_:							int	=						message.lower()
							UpperCamelCase_:							Tuple	=						message.replace(""" """						,	""""""      )
							UpperCamelCase_:							int	=						message.replace("""j"""						,	"""i"""      )

							UpperCamelCase_:							Any	=						np.empty((2, len(snake_case_      ))      )
							for letter_index in range(len(snake_case_      )      ):
											UpperCamelCase_:							Optional[int]	=						self.letter_to_numbers(message[letter_index]      )

											UpperCamelCase_:							Union[str, Any]	=						numbers[0]
											UpperCamelCase_:							Union[str, Any]	=						numbers[1]

							UpperCamelCase_:							Optional[int]	=						first_step.reshape(2 * len(snake_case_      )      )
							UpperCamelCase_:							int	=						''
							for numbers_index in range(len(snake_case_      )      ):
											UpperCamelCase_:							str	=						int(second_step[numbers_index * 2]      )
											UpperCamelCase_:							str	=						int(second_step[(numbers_index * 2) + 1]      )
											UpperCamelCase_:							Tuple	=						self.numbers_to_letter(snake_case_						,	snake_case_      )
											UpperCamelCase_:							Tuple	=						encoded_message + letter

							return encoded_message




			def       lowerCAmelCase__	(       self :       int						,	snake_case_ :       List[str]      ):
							UpperCamelCase_:							Optional[int]	=						message.lower()
							message.replace(""" """						,	""""""      )
							UpperCamelCase_:							Tuple	=						np.empty(2 * len(snake_case_      )      )
							for letter_index in range(len(snake_case_      )      ):
											UpperCamelCase_:							Optional[Any]	=						self.letter_to_numbers(message[letter_index]      )
											UpperCamelCase_:							Optional[int]	=						numbers[0]
											UpperCamelCase_:							Dict	=						numbers[1]

							UpperCamelCase_:							Optional[int]	=						first_step.reshape((2, len(snake_case_      ))      )
							UpperCamelCase_:							List[str]	=						''
							for numbers_index in range(len(snake_case_      )      ):
											UpperCamelCase_:							List[Any]	=						int(second_step[0, numbers_index]      )
											UpperCamelCase_:							Optional[int]	=						int(second_step[1, numbers_index]      )
											UpperCamelCase_:							Tuple	=						self.numbers_to_letter(snake_case_						,	snake_case_      )
											UpperCamelCase_:							str	=						decoded_message + letter

							return decoded_message








import random







def        A__					(						lowerCamelCase     ,    lowerCamelCase     ,    lowerCamelCase = False						)  ->	dict:
				UpperCamelCase_:							dict	=						{i: [] for i in range(lowerCamelCase						)}

				# if probability is greater or equal than 1, then generate a complete graph
				if probability >= 1:
								return complete_graph(lowerCamelCase						)
				# if probability is lower or equal than 0, then return a graph without edges
				if probability <= 0:
								return graph

				# for each couple of nodes, add an edge from u to v
				# if the number randomly generated is greater than probability probability
				for i in range(lowerCamelCase						):
								for j in range(i + 1     ,    lowerCamelCase						):
												if random.random() < probability:
																graph[i].append(lowerCamelCase						)
																if not directed:
																				# if the graph is undirected, add an edge in from j to i, either
																				graph[j].append(lowerCamelCase						)
				return graph







def        A__					(						lowerCamelCase						)  ->	dict:
				return {
				    i: [j for j in range(lowerCamelCase						) if i != j] for i in range(lowerCamelCase						)
				}


if __name__ == "__main__":
							import doctest

							doctest.testmod()






