




'''simple docstring'''







import numpy as np






def 						_lowercase						(      lowercase_		,				lowercase_="utf-8"		,				lowercase_="surrogatepass"    ):



		'''simple docstring'''







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






def 						_lowercase						(      lowercase_		,				lowercase_="utf-8"		,				lowercase_="surrogatepass"    ):



		'''simple docstring'''







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






def 						_lowercase						(      lowercase_		,				lowercase_    ):



		'''simple docstring'''







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

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

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

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

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

				qtd_bp += 1

		# Mount the message
		_snake_case      			=			0  # parity bit counter
		for x in range(0		,				size_par + len(UpperCamelCase_    )    ):
				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 						_lowercase						(      lowercase_		,				lowercase_    ):



		'''simple docstring'''







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

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

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

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

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

		_snake_case      			=			parity_received == parity
		return data_output, ack












from itertools import compress, repeat
from math import ceil, sqrt




def 			lowerCAmelCase_			(				UpperCamelCase_	)  ->		list[int]:

       if num <= 2:
              return []
       if num == 3:
              return [2]

       # Odd sieve for numbers in range [3, num - 1]
       UpperCamelCase_ 							=	bytearray(b"\x01"	) * ((num >> 1) - 1)

       for i in range(3       ,		int(sqrt(UpperCamelCase_	)	) + 1       ,		2	):
              if sieve[(i >> 1) - 1]:
                     UpperCamelCase_ 							=	i**2
                     UpperCamelCase_ 							=	repeat(
                         0       ,		ceil((num - i_squared) / (i << 1)	)	)

       return [2] + list(compress(range(3       ,		UpperCamelCase_       ,		2	)       ,		UpperCamelCase_	)	)


if __name__ == "__main__":
     import doctest

     doctest.testmod()

