




import math







def   _snake_case    (       lowercase__	):
				_lowerCamelCase  :    str					=					[]
				_lowerCamelCase  :    List[str]					=					2
				_lowerCamelCase  :    Any					=					int(math.sqrt(lowercase__	)	)  # Size of every segment
				_lowerCamelCase  :    Optional[int]					=					[True] * (end + 1)
				_lowerCamelCase  :    Union[str, Any]					=					[]

				while start <= end:
								if temp[start] is True:
												in_prime.append(lowercase__	)
												for i in range(start * start							,					end + 1							,					lowercase__	):
																_lowerCamelCase  :    str					=					False
								start += 1
				prime += in_prime

				_lowerCamelCase  :    Optional[Any]					=					end + 1
				_lowerCamelCase  :    List[Any]					=					min(2 * end							,					lowercase__	)

				while low <= n:
								_lowerCamelCase  :    List[str]					=					[True] * (high - low + 1)
								for each in in_prime:
												_lowerCamelCase  :    Optional[Any]					=					math.floor(low / each	) * each
												if t < low:
																t += each

												for j in range(lowercase__							,					high + 1							,					lowercase__	):
																_lowerCamelCase  :    Optional[Any]					=					False

								for j in range(len(lowercase__	)	):
												if temp[j] is True:
																prime.append(j + low	)

								_lowerCamelCase  :    Optional[int]					=					high + 1
								_lowerCamelCase  :    List[Any]					=					min(high + end							,					lowercase__	)

				return prime
print(sieve(10**6))





"""simple docstring"""






from math import pow, sqrt







def   _snake_case    (       *lowercase__	):
				_lowerCamelCase  :    Dict					=					len(lowercase__	) > 0 and all(value > 0.0 for value in values	)
				return result







def   _snake_case    (       lowercase__							,					lowercase__	):
				return (
				    round(sqrt(molar_mass_a / molar_mass_a	)							,					6	)
				    if validate(lowercase__							,					lowercase__	)
				    else ValueError('Input Error: Molar mass values must greater than 0.'	)
				)







def   _snake_case    (       lowercase__							,					lowercase__							,					lowercase__	):
				return (
				    round(effusion_rate * sqrt(molar_mass_a / molar_mass_a	)							,					6	)
				    if validate(lowercase__							,					lowercase__							,					lowercase__	)
				    else ValueError(
				        'Input Error: Molar mass and effusion rate values must greater than 0.'	)
				)







def   _snake_case    (       lowercase__							,					lowercase__							,					lowercase__	):
				return (
				    round(effusion_rate / sqrt(molar_mass_a / molar_mass_a	)							,					6	)
				    if validate(lowercase__							,					lowercase__							,					lowercase__	)
				    else ValueError(
				        'Input Error: Molar mass and effusion rate values must greater than 0.'	)
				)







def   _snake_case    (       lowercase__							,					lowercase__							,					lowercase__	):
				return (
				    round(molar_mass / pow(effusion_rate_a / effusion_rate_a							,					2	)							,					6	)
				    if validate(lowercase__							,					lowercase__							,					lowercase__	)
				    else ValueError(
				        'Input Error: Molar mass and effusion rate values must greater than 0.'	)
				)







def   _snake_case    (       lowercase__							,					lowercase__							,					lowercase__	):
				return (
				    round(pow(effusion_rate_a / effusion_rate_a							,					2	) / molar_mass							,					6	)
				    if validate(lowercase__							,					lowercase__							,					lowercase__	)
				    else ValueError(
				        'Input Error: Molar mass and effusion rate values must greater than 0.'	)
				)