




"""simple docstring"""





from __future__ import annotations

import math

def 					_UpperCamelCase    (			UpperCamelCase							)			->			list[int]:


			"""simple docstring"""

			if num <= 0:
						__UpperCAmelCase	: str		=					f"{num}: Invalid input, please enter a positive integer."
						raise ValueError(UpperCamelCase							)

			__UpperCAmelCase	: List[str]		=					[True] * (num + 1)
			__UpperCAmelCase	: List[str]		=					[]
			__UpperCAmelCase	: Union[str, Any]		=					2
			__UpperCAmelCase	: Union[str, Any]		=					int(math.sqrt(UpperCamelCase							)							)

			while start <= end:
						# If start is a prime
						if sieve[start] is True:
									prime.append(UpperCamelCase							)

									# Set multiples of start be False
									for i in range(start * start				,       num + 1				,       UpperCamelCase							):
												if sieve[i] is True:
															__UpperCAmelCase	: Optional[Any]		=					False

						start += 1

			for j in range(end + 1				,       num + 1							):
						if sieve[j] is True:
									prime.append(UpperCamelCase							)

			return prime


if __name__ == "__main__":
					print(prime_sieve(int(input("""Enter a positive integer: """).strip())))








"""simple docstring"""





from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter

def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase = 1 / sqrt(2							)							)			->			IIRFilter:


			"""simple docstring"""
			__UpperCAmelCase	: List[str]		=					tau * frequency / samplerate
			__UpperCAmelCase	: Optional[int]		=					sin(UpperCamelCase							)
			__UpperCAmelCase	: Any		=					cos(UpperCamelCase							)
			__UpperCAmelCase	: Tuple		=					_sin / (2 * q_factor)

			__UpperCAmelCase	: Optional[Any]		=					(1 - _cos) / 2
			__UpperCAmelCase	: Any		=					1 - _cos

			__UpperCAmelCase	: List[str]		=					1 + alpha
			__UpperCAmelCase	: List[Any]		=					-2 * _cos
			__UpperCAmelCase	: Dict		=					1 - alpha

			__UpperCAmelCase	: str		=					IIRFilter(2							)
			filt.set_coefficients([aa, aa, aa]				,       [ba, ba, ba]							)
			return filt

def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase = 1 / sqrt(2							)							)			->			IIRFilter:


			"""simple docstring"""
			__UpperCAmelCase	: int		=					tau * frequency / samplerate
			__UpperCAmelCase	: Optional[Any]		=					sin(UpperCamelCase							)
			__UpperCAmelCase	: Dict		=					cos(UpperCamelCase							)
			__UpperCAmelCase	: Tuple		=					_sin / (2 * q_factor)

			__UpperCAmelCase	: Dict		=					(1 + _cos) / 2
			__UpperCAmelCase	: Tuple		=					-1 - _cos

			__UpperCAmelCase	: Any		=					1 + alpha
			__UpperCAmelCase	: int		=					-2 * _cos
			__UpperCAmelCase	: int		=					1 - alpha

			__UpperCAmelCase	: Union[str, Any]		=					IIRFilter(2							)
			filt.set_coefficients([aa, aa, aa]				,       [ba, ba, ba]							)
			return filt

def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase = 1 / sqrt(2							)							)			->			IIRFilter:


			"""simple docstring"""
			__UpperCAmelCase	: Tuple		=					tau * frequency / samplerate
			__UpperCAmelCase	: Tuple		=					sin(UpperCamelCase							)
			__UpperCAmelCase	: List[str]		=					cos(UpperCamelCase							)
			__UpperCAmelCase	: List[Any]		=					_sin / (2 * q_factor)

			__UpperCAmelCase	: Any		=					_sin / 2
			__UpperCAmelCase	: Optional[int]		=					0
			__UpperCAmelCase	: int		=					-ba

			__UpperCAmelCase	: Dict		=					1 + alpha
			__UpperCAmelCase	: List[str]		=					-2 * _cos
			__UpperCAmelCase	: int		=					1 - alpha

			__UpperCAmelCase	: int		=					IIRFilter(2							)
			filt.set_coefficients([aa, aa, aa]				,       [ba, ba, ba]							)
			return filt

def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase = 1 / sqrt(2							)							)			->			IIRFilter:


			"""simple docstring"""
			__UpperCAmelCase	: str		=					tau * frequency / samplerate
			__UpperCAmelCase	: List[Any]		=					sin(UpperCamelCase							)
			__UpperCAmelCase	: Any		=					cos(UpperCamelCase							)
			__UpperCAmelCase	: List[str]		=					_sin / (2 * q_factor)

			__UpperCAmelCase	: Optional[Any]		=					1 - alpha
			__UpperCAmelCase	: Tuple		=					-2 * _cos
			__UpperCAmelCase	: List[Any]		=					1 + alpha

			__UpperCAmelCase	: str		=					IIRFilter(2							)
			filt.set_coefficients([ba, ba, ba]				,       [ba, ba, ba]							)
			return filt

def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase = 1 / sqrt(2							)				,       )			->			IIRFilter:


			"""simple docstring"""
			__UpperCAmelCase	: Dict		=					tau * frequency / samplerate
			__UpperCAmelCase	: Optional[int]		=					sin(UpperCamelCase							)
			__UpperCAmelCase	: Optional[Any]		=					cos(UpperCamelCase							)
			__UpperCAmelCase	: List[Any]		=					_sin / (2 * q_factor)
			__UpperCAmelCase	: List[Any]		=					10 ** (gain_db / 40)

			__UpperCAmelCase	: List[str]		=					1 + alpha * big_a
			__UpperCAmelCase	: Optional[Any]		=					-2 * _cos
			__UpperCAmelCase	: int		=					1 - alpha * big_a
			__UpperCAmelCase	: Optional[int]		=					1 + alpha / big_a
			__UpperCAmelCase	: Union[str, Any]		=					-2 * _cos
			__UpperCAmelCase	: Dict		=					1 - alpha / big_a

			__UpperCAmelCase	: Dict		=					IIRFilter(2							)
			filt.set_coefficients([aa, aa, aa]				,       [ba, ba, ba]							)
			return filt

def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase = 1 / sqrt(2							)				,       )			->			IIRFilter:


			"""simple docstring"""
			__UpperCAmelCase	: str		=					tau * frequency / samplerate
			__UpperCAmelCase	: int		=					sin(UpperCamelCase							)
			__UpperCAmelCase	: Optional[Any]		=					cos(UpperCamelCase							)
			__UpperCAmelCase	: str		=					_sin / (2 * q_factor)
			__UpperCAmelCase	: str		=					10 ** (gain_db / 40)
			__UpperCAmelCase	: Union[str, Any]		=					(big_a + 1) - (big_a - 1) * _cos
			__UpperCAmelCase	: Optional[int]		=					(big_a + 1) + (big_a - 1) * _cos
			__UpperCAmelCase	: List[str]		=					(big_a - 1) - (big_a + 1) * _cos
			__UpperCAmelCase	: List[Any]		=					(big_a - 1) + (big_a + 1) * _cos
			__UpperCAmelCase	: Optional[Any]		=					2 * sqrt(UpperCamelCase							) * alpha

			__UpperCAmelCase	: Tuple		=					big_a * (pmc + aaa)
			__UpperCAmelCase	: Union[str, Any]		=					2 * big_a * mpc
			__UpperCAmelCase	: Optional[int]		=					big_a * (pmc - aaa)
			__UpperCAmelCase	: Any		=					ppmc + aaa
			__UpperCAmelCase	: Dict		=					-2 * pmpc
			__UpperCAmelCase	: Any		=					ppmc - aaa

			__UpperCAmelCase	: str		=					IIRFilter(2							)
			filt.set_coefficients([aa, aa, aa]				,       [ba, ba, ba]							)
			return filt





def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase = 1 / sqrt(2							)				,       )			->			IIRFilter:


			"""simple docstring"""
			__UpperCAmelCase	: Dict		=					tau * frequency / samplerate
			__UpperCAmelCase	: Optional[int]		=					sin(UpperCamelCase							)
			__UpperCAmelCase	: Dict		=					cos(UpperCamelCase							)
			__UpperCAmelCase	: str		=					_sin / (2 * q_factor)
			__UpperCAmelCase	: int		=					10 ** (gain_db / 40)
			__UpperCAmelCase	: Optional[Any]		=					(big_a + 1) - (big_a - 1) * _cos
			__UpperCAmelCase	: Optional[int]		=					(big_a + 1) + (big_a - 1) * _cos
			__UpperCAmelCase	: Union[str, Any]		=					(big_a - 1) - (big_a + 1) * _cos
			__UpperCAmelCase	: Tuple		=					(big_a - 1) + (big_a + 1) * _cos
			__UpperCAmelCase	: Optional[Any]		=					2 * sqrt(UpperCamelCase							) * alpha

			__UpperCAmelCase	: Tuple		=					big_a * (ppmc + aaa)
			__UpperCAmelCase	: Any		=					-2 * big_a * pmpc
			__UpperCAmelCase	: int		=					big_a * (ppmc - aaa)
			__UpperCAmelCase	: int		=					pmc + aaa
			__UpperCAmelCase	: Tuple		=					2 * mpc
			__UpperCAmelCase	: Union[str, Any]		=					pmc - aaa

			__UpperCAmelCase	: Any		=					IIRFilter(2							)
			filt.set_coefficients([aa, aa, aa]				,       [ba, ba, ba]							)
			return filt


