



import numpy as np



def        __a     (    lowerCAmelCase_   :					Union[str, Any]			,lowerCAmelCase_   :					Union[str, Any]="utf-8"			,lowerCAmelCase_   :					str="surrogatepass"				)      -> List[str]:






						'''simple docstring'''



						UpperCAmelCase_=   bin(int.from_bytes(text.encode(lowerCamelCase_			,lowerCamelCase_				)			,"""big"""				)				)[2:]
						return bits.zfill(8 * ((len(lowerCamelCase_				) + 7) // 8)				)



def        __a     (    lowerCAmelCase_   :					Optional[Any]			,lowerCAmelCase_   :					List[Any]="utf-8"			,lowerCAmelCase_   :					List[str]="surrogatepass"				)      -> Any:






						'''simple docstring'''



						UpperCAmelCase_=   int(lowerCamelCase_			,2				)
						return n.to_bytes((n.bit_length() + 7) // 8			,"""big"""				).decode(lowerCamelCase_			,lowerCamelCase_				) or "\0"



def        __a     (    lowerCAmelCase_   :					Tuple			,lowerCAmelCase_   :					List[Any]				)      -> List[str]:






						'''simple docstring'''



						if size_par + len(lowerCamelCase_				) <= 2**size_par - (len(lowerCamelCase_				) - 1):
												raise ValueError("""size of parity don\'t match with size of data"""				)

						UpperCAmelCase_=   []
						UpperCAmelCase_=   []
						UpperCAmelCase_=   [bin(lowerCamelCase_				)[2:] for x in range(1			,size_par + len(lowerCamelCase_				) + 1				)]

						# sorted information data for the size of the output data
						UpperCAmelCase_=   []
						# data position template + parity
						UpperCAmelCase_=   []
						# parity bit counter
						UpperCAmelCase_=   0
						# counter position of data bits
						UpperCAmelCase_=   0

						for x in range(1			,size_par + len(lowerCamelCase_				) + 1				):
												# Performs a template of bit positions - who should be given,
												# and who should be parity
												if qtd_bp < size_par:
																		if (np.log(lowerCamelCase_				) / np.log(2				)).is_integer():
																								data_out_gab.append("""P"""				)
																								UpperCAmelCase_=   qtd_bp + 1
																		else:
																								data_out_gab.append("""D"""				)
												else:
																		data_out_gab.append("""D"""				)

												# Sorts the data to the new output size
												if data_out_gab[-1] == "D":
																		data_ord.append(data[cont_data]				)
																		cont_data += 1
												else:
																		data_ord.append(lowerCamelCase_				)

    # Calculates parity
						UpperCAmelCase_=   0  # parity bit counter
						for bp in range(1			,size_par + 1				):
												# Bit counter one for a given parity
												UpperCAmelCase_=   0
												# counter to control the loop reading
												UpperCAmelCase_=   0
												for x in data_ord:
																		if x is not None:
																								try:
																														UpperCAmelCase_=   (bin_pos[cont_loop])[-1 * (bp)]
																								except IndexError:
																														UpperCAmelCase_=   """0"""
																								if aux == "1" and x == "1":
																														cont_bo += 1
																		cont_loop += 1
												parity.append(cont_bo % 2				)

												qtd_bp += 1

						# Mount the message
						UpperCAmelCase_=   0  # parity bit counter
						for x in range(0			,size_par + len(lowerCamelCase_				)				):
												if data_ord[x] is None:
																		data_out.append(str(parity[cont_bp]				)				)
																		cont_bp += 1
												else:
																		data_out.append(data_ord[x]				)

						return data_out



def        __a     (    lowerCAmelCase_   :					Optional[Any]			,lowerCAmelCase_   :					Optional[int]				)      -> Tuple:






						'''simple docstring'''



						UpperCAmelCase_=   []
						# Parity bit counter
						UpperCAmelCase_=   0
						# Counter p data bit reading
						UpperCAmelCase_=   0
						# list of parity received
						UpperCAmelCase_=   []
						UpperCAmelCase_=   []

						for x in range(1			,len(lowerCamelCase_				) + 1				):
												# Performs a template of bit positions - who should be given,
												#  and who should be parity
												if qtd_bp < size_par and (np.log(lowerCamelCase_				) / np.log(2				)).is_integer():
																		data_out_gab.append("""P"""				)
																		UpperCAmelCase_=   qtd_bp + 1
												else:
																		data_out_gab.append("""D"""				)

												# Sorts the data to the new output size
												if data_out_gab[-1] == "D":
																		data_output.append(data[cont_data]				)
												else:
																		parity_received.append(data[cont_data]				)
												cont_data += 1

						# -----------calculates the parity with the data
						UpperCAmelCase_=   []
						UpperCAmelCase_=   []
						UpperCAmelCase_=   [bin(lowerCamelCase_				)[2:] for x in range(1			,size_par + len(lowerCamelCase_				) + 1				)]

						#  sorted information data for the size of the output data
						UpperCAmelCase_=   []
						# Data position feedback + parity
						UpperCAmelCase_=   []
						# Parity bit counter
						UpperCAmelCase_=   0
						# Counter p data bit reading
						UpperCAmelCase_=   0

						for x in range(1			,size_par + len(lowerCamelCase_				) + 1				):
												# Performs a template position of bits - who should be given,
												# and who should be parity
												if qtd_bp < size_par and (np.log(lowerCamelCase_				) / np.log(2				)).is_integer():
																		data_out_gab.append("""P"""				)
																		UpperCAmelCase_=   qtd_bp + 1
												else:
																		data_out_gab.append("""D"""				)

												# Sorts the data to the new output size
												if data_out_gab[-1] == "D":
																		data_ord.append(data_output[cont_data]				)
																		cont_data += 1
												else:
																		data_ord.append(lowerCamelCase_				)

    # Calculates parity
						UpperCAmelCase_=   0  # parity bit counter
						for bp in range(1			,size_par + 1				):
												# Bit counter one for a certain parity
												UpperCAmelCase_=   0
												# Counter to control loop reading
												UpperCAmelCase_=   0
												for x in data_ord:
																		if x is not None:
																								try:
																														UpperCAmelCase_=   (bin_pos[cont_loop])[-1 * (bp)]
																								except IndexError:
																														UpperCAmelCase_=   """0"""
																								if aux == "1" and x == "1":
																														cont_bo += 1
																		cont_loop += 1
												parity.append(str(cont_bo % 2				)				)

												qtd_bp += 1

						# Mount the message
						UpperCAmelCase_=   0  # Parity bit counter
						for x in range(0			,size_par + len(lowerCamelCase_				)				):
												if data_ord[x] is None:
																		data_out.append(str(parity[cont_bp]				)				)
																		cont_bp += 1
												else:
																		data_out.append(data_ord[x]				)

						UpperCAmelCase_=   parity_received == parity
						return data_output, ack











'''simple docstring'''



import math




def       _lowerCAmelCase  ( lowerCamelCase_	:     int ):

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5						,				int(math.sqrt(lowerCamelCase_ ) + 1 )						,				6 ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True




def       _lowerCAmelCase  ( lowerCamelCase_	:     int = 6_0_0_8_5_1_4_7_5_1_4_3 ):

			try:
						__lowercase   =							int(lowerCamelCase_ )
			except (TypeError, ValueError):
						raise TypeError('''Parameter n must be int or castable to int.''' )
			if n <= 0:
						raise ValueError('''Parameter n must be greater than or equal to one.''' )
			__lowercase   =							0
			if is_prime(lowerCamelCase_ ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(lowerCamelCase_ ):
						return n
			for i in range(3						,				int(math.sqrt(lowerCamelCase_ ) ) + 1						,				2 ):
						if n % i == 0:
									if is_prime(n // i ):
												__lowercase   =							n // i
												break
									elif is_prime(lowerCamelCase_ ):
												__lowercase   =							i
			return max_number


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





