

from __future__ import annotations

import math







def       A_				(   _UpperCAmelCase   ):

						if num <= 0:
												SCREAMING_SNAKE_CASE_:			Union[str, Any]  		=	f"{num}: Invalid input, please enter a positive integer."
												raise ValueError(_UpperCAmelCase   )

						SCREAMING_SNAKE_CASE_:			Optional[int]  		=	[True] * (num + 1)
						SCREAMING_SNAKE_CASE_:			str  		=	[]
						SCREAMING_SNAKE_CASE_:			Union[str, Any]  		=	2
						SCREAMING_SNAKE_CASE_:			int  		=	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:
																														SCREAMING_SNAKE_CASE_:			Tuple  		=	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())))









import doctest
from collections import deque

import numpy as np



class   __lowercase    :




			"""simple docstring"""







			def __init__(			self  :					Union[str, Any]):
									SCREAMING_SNAKE_CASE_:			int  		=	[2, 1, 2, -1]
									SCREAMING_SNAKE_CASE_:			Optional[Any]  		=	[1, 2, 3, 4]




			def 	_SCREAMING_SNAKE_CASE      (			self  :					Tuple):
									SCREAMING_SNAKE_CASE_:			Any  		=	len(self.first_signal)
									SCREAMING_SNAKE_CASE_:			Dict  		=	len(self.second_signal)

									SCREAMING_SNAKE_CASE_:			Union[str, Any]  		=	max(lowerCAmelCase__       ,						lowerCAmelCase__)

									# create a zero matrix of max_length x max_length
									SCREAMING_SNAKE_CASE_:			List[Any]  		=	[[0] * max_length for i in range(lowerCAmelCase__)]

									# fills the smaller signal with zeros to make both signals of same length
									if length_first_signal < length_second_signal:
															self.first_signal += [0] * (max_length - length_first_signal)
									elif length_first_signal > length_second_signal:
															self.second_signal += [0] * (max_length - length_second_signal)
									for i in range(lowerCAmelCase__):
															SCREAMING_SNAKE_CASE_:			Tuple  		=	deque(self.second_signal)
															rotated_signal.rotate(lowerCAmelCase__)
															for j, item in enumerate(lowerCAmelCase__):
																					matrix[i][j] += item

        # multiply the matrix with the first signal
									SCREAMING_SNAKE_CASE_:			Optional[Any]  		=	np.matmul(np.transpose(lowerCAmelCase__)       ,						np.transpose(self.first_signal))

									# rounding-off to two decimal places
									return [round(lowerCAmelCase__       ,						2) for i in final_signal]


if __name__ == "__main__":
						doctest.testmod()






