





"""simple docstring"""


import numpy as np

def     UpperCamelCase       (SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE="utf-8"       ,    SCREAMING_SNAKE_CASE="surrogatepass"    ):
						UpperCamelCase							:		Union[str, Any]							      = bin(int.from_bytes(text.encode(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    )       ,    """big"""    )    )[2:]
						return bits.zfill(8 * ((len(SCREAMING_SNAKE_CASE    ) + 7) // 8)    )

def     UpperCamelCase       (SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE="utf-8"       ,    SCREAMING_SNAKE_CASE="surrogatepass"    ):
						UpperCamelCase							:		str							      = int(SCREAMING_SNAKE_CASE       ,    2    )
						return n.to_bytes((n.bit_length() + 7) // 8       ,    """big"""    ).decode(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ) or "\0"

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

						UpperCamelCase							:		Tuple							      = []
						UpperCamelCase							:		Dict							      = []
						UpperCamelCase							:		Union[str, Any]							      = [bin(SCREAMING_SNAKE_CASE    )[2:] for x in range(1       ,    size_par + len(SCREAMING_SNAKE_CASE    ) + 1    )]

						# sorted information data for the size of the output data
						UpperCamelCase							:		List[str]							      = []
						# data position template + parity
						UpperCamelCase							:		Union[str, Any]							      = []
						# parity bit counter
						UpperCamelCase							:		List[Any]							      = 0
						# counter position of data bits
						UpperCamelCase							:		str							      = 0

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

    # Calculates parity
						UpperCamelCase							:		Optional[Any]							      = 0  # parity bit counter
						for bp in range(1       ,    size_par + 1    ):
												# Bit counter one for a given parity
												UpperCamelCase							:		List[str]							      = 0
												# counter to control the loop reading
												UpperCamelCase							:		Any							      = 0
												for x in data_ord:
																		if x is not None:
																								try:
																														UpperCamelCase							:		str							      = (bin_pos[cont_loop])[-1 * (bp)]
																								except IndexError:
																														UpperCamelCase							:		str							      = """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							:		Optional[int]							      = 0  # parity bit counter
						for x in range(0       ,    size_par + len(SCREAMING_SNAKE_CASE    )    ):
												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     UpperCamelCase       (SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
						UpperCamelCase							:		Optional[int]							      = []
						# Parity bit counter
						UpperCamelCase							:		Tuple							      = 0
						# Counter p data bit reading
						UpperCamelCase							:		Optional[int]							      = 0
						# list of parity received
						UpperCamelCase							:		int							      = []
						UpperCamelCase							:		Dict							      = []

						for x in range(1       ,    len(SCREAMING_SNAKE_CASE    ) + 1    ):
												# Performs a template of bit positions - who should be given,
												#  and who should be parity
												if qtd_bp < size_par and (np.log(SCREAMING_SNAKE_CASE    ) / np.log(2    )).is_integer():
																		data_out_gab.append("""P"""    )
																		UpperCamelCase							:		str							      = 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							:		Dict							      = []
						UpperCamelCase							:		Tuple							      = []
						UpperCamelCase							:		int							      = [bin(SCREAMING_SNAKE_CASE    )[2:] for x in range(1       ,    size_par + len(SCREAMING_SNAKE_CASE    ) + 1    )]

						#  sorted information data for the size of the output data
						UpperCamelCase							:		List[Any]							      = []
						# Data position feedback + parity
						UpperCamelCase							:		Any							      = []
						# Parity bit counter
						UpperCamelCase							:		str							      = 0
						# Counter p data bit reading
						UpperCamelCase							:		Tuple							      = 0

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

    # Calculates parity
						UpperCamelCase							:		Dict							      = 0  # parity bit counter
						for bp in range(1       ,    size_par + 1    ):
												# Bit counter one for a certain parity
												UpperCamelCase							:		Dict							      = 0
												# Counter to control loop reading
												UpperCamelCase							:		Optional[Any]							      = 0
												for x in data_ord:
																		if x is not None:
																								try:
																														UpperCamelCase							:		Any							      = (bin_pos[cont_loop])[-1 * (bp)]
																								except IndexError:
																														UpperCamelCase							:		Optional[int]							      = """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							:		Dict							      = 0  # Parity bit counter
						for x in range(0       ,    size_par + len(SCREAMING_SNAKE_CASE    )    ):
												if data_ord[x] is None:
																		data_out.append(str(parity[cont_bp]    )    )
																		cont_bp += 1
												else:
																		data_out.append(data_ord[x]    )

						UpperCamelCase							:		str							      = parity_received == parity
						return data_output, ack










"""simple docstring"""


from __future__ import annotations

def     UpperCamelCase       (SCREAMING_SNAKE_CASE    ):
						UpperCamelCase							:		Tuple							      = [0] * max_one

						for i in range(0       ,    SCREAMING_SNAKE_CASE    ):
												UpperCamelCase							:		Union[str, Any]							      = i

						for i in range(2       ,    SCREAMING_SNAKE_CASE    ):
												if totients[i] == i:
																		for j in range(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
																								totients[j] -= totients[j] // i

						return totients

def     UpperCamelCase       (SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
						return sorted(str(SCREAMING_SNAKE_CASE    )    ) == sorted(str(SCREAMING_SNAKE_CASE    )    )

def     UpperCamelCase       (SCREAMING_SNAKE_CASE = 1000_0000    ):
						UpperCamelCase							:		List[str]							      = 1  # i
						UpperCamelCase							:		Optional[int]							      = 0  # φ(i)
						UpperCamelCase							:		List[str]							      = get_totients(max_n + 1    )

						for i in range(2       ,    max_n + 1    ):
												UpperCamelCase							:		Tuple							      = totients[i]

												if i * min_denominator < min_numerator * t and has_same_digits(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
																		UpperCamelCase							:		str							      = i
																		UpperCamelCase							:		Tuple							      = t

						return min_numerator


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



