


"""simple docstring"""






from collections.abc import Generator
from math import sin
def      lowerCamelCase       (     _UpperCamelCase		:      bytes							)		->       bytes:

							'''simple docstring'''



							if len(_UpperCamelCase							) != 3_2:
														raise ValueError("""Input must be of length 32"""							)

							__UpperCAmelCase   :						Optional[Any]      							=					b""""""
							for i in [3, 2, 1, 0]:
														little_endian += string_aa[8 * i : 8 * i + 8]
							return little_endian
def      lowerCamelCase       (     _UpperCamelCase		:      int							)		->       bytes:

							'''simple docstring'''



							if i < 0:
														raise ValueError("""Input must be non-negative"""							)

							__UpperCAmelCase   :						int      							=					format(_UpperCamelCase       ,			"""08x"""							)[-8:]
							__UpperCAmelCase   :						str      							=					b""""""
							for i in [3, 2, 1, 0]:
														little_endian_hex += hex_rep[2 * i : 2 * i + 2].encode("""utf-8"""							)
							return little_endian_hex
def      lowerCamelCase       (     _UpperCamelCase		:      bytes							)		->       bytes:

							'''simple docstring'''



							__UpperCAmelCase   :						List[Any]      							=					b""""""
							for char in message:
														bit_string += format(_UpperCamelCase       ,			"""08b"""							).encode("""utf-8"""							)
							__UpperCAmelCase   :						str      							=					format(len(_UpperCamelCase							)       ,			"""064b"""							).encode("""utf-8"""							)

							# Pad bit_string to a multiple of 512 chars
							bit_string += b"1"
							while len(_UpperCamelCase							) % 5_1_2 != 4_4_8:
														bit_string += b"0"
							bit_string += to_little_endian(start_len[3_2:]							) + to_little_endian(start_len[:3_2]							)

							return bit_string
def      lowerCamelCase       (     _UpperCamelCase		:      bytes							)		->       Generator[list[int], None, None]:

							'''simple docstring'''



							if len(_UpperCamelCase							) % 5_1_2 != 0:
														raise ValueError("""Input must have length that's a multiple of 512"""							)

							for pos in range(0       ,			len(_UpperCamelCase							)       ,			5_1_2							):
														__UpperCAmelCase   :						List[str]      							=					bit_string[pos : pos + 5_1_2]
														__UpperCAmelCase   :						Tuple      							=					[]
														for i in range(0       ,			5_1_2       ,			3_2							):
																					block_words.append(int(to_little_endian(block[i : i + 3_2]							)       ,			2							)							)
														yield block_words
def      lowerCamelCase       (     _UpperCamelCase		:      int							)		->       int:

							'''simple docstring'''



							if i < 0:
														raise ValueError("""Input must be non-negative"""							)

							__UpperCAmelCase   :						List[str]      							=					format(_UpperCamelCase       ,			"""032b"""							)
							__UpperCAmelCase   :						int      							=					""""""
							for c in i_str:
														new_str += "1" if c == "0" else "0"
							return int(_UpperCamelCase       ,			2							)
def      lowerCamelCase       (     _UpperCamelCase		:      int       ,			_UpperCamelCase		:      int							)		->       int:

							'''simple docstring'''



							return (a + b) % 2**3_2
def      lowerCamelCase       (     _UpperCamelCase		:      int       ,			_UpperCamelCase		:      int							)		->       int:

							'''simple docstring'''



							if i < 0:
														raise ValueError("""Input must be non-negative"""							)
							if shift < 0:
														raise ValueError("""Shift must be non-negative"""							)
							return ((i << shift) ^ (i >> (3_2 - shift))) % 2**3_2
def      lowerCamelCase       (     _UpperCamelCase		:      bytes							)		->       bytes:

							'''simple docstring'''



							__UpperCAmelCase   :						Dict      							=					preprocess(_UpperCamelCase							)

							__UpperCAmelCase   :						int      							=					[int(2**3_2 * abs(sin(i + 1							)							)							) for i in range(6_4							)]

							# Starting states
							__UpperCAmelCase   :						Dict      							=					0x67_45_23_01
							__UpperCAmelCase   :						Dict      							=					0xef_cd_ab_89
							__UpperCAmelCase   :						Any      							=					0x98_ba_dc_fe
							__UpperCAmelCase   :						Union[str, Any]      							=					0x10_32_54_76

							__UpperCAmelCase   :						List[Any]      							=					[
							    7,
							    1_2,
							    1_7,
							    2_2,
							    7,
							    1_2,
							    1_7,
							    2_2,
							    7,
							    1_2,
							    1_7,
							    2_2,
							    7,
							    1_2,
							    1_7,
							    2_2,
							    5,
							    9,
							    1_4,
							    2_0,
							    5,
							    9,
							    1_4,
							    2_0,
							    5,
							    9,
							    1_4,
							    2_0,
							    5,
							    9,
							    1_4,
							    2_0,
							    4,
							    1_1,
							    1_6,
							    2_3,
							    4,
							    1_1,
							    1_6,
							    2_3,
							    4,
							    1_1,
							    1_6,
							    2_3,
							    4,
							    1_1,
							    1_6,
							    2_3,
							    6,
							    1_0,
							    1_5,
							    2_1,
							    6,
							    1_0,
							    1_5,
							    2_1,
							    6,
							    1_0,
							    1_5,
							    2_1,
							    6,
							    1_0,
							    1_5,
							    2_1,
							]

							# Process bit string in chunks, each with 16 32-char words
							for block_words in get_block_words(_UpperCamelCase							):
														__UpperCAmelCase   :						List[str]      							=					aa
														__UpperCAmelCase   :						Tuple      							=					ba
														__UpperCAmelCase   :						List[str]      							=					ca
														__UpperCAmelCase   :						Union[str, Any]      							=					da

														# Hash current chunk
														for i in range(6_4							):
																					if i <= 1_5:
																												# f = (b & c) | (not_32(b) & d)     # Alternate definition for f
																												__UpperCAmelCase   :						Tuple      							=					d ^ (b & (c ^ d))
																												__UpperCAmelCase   :						Dict      							=					i
																					elif i <= 3_1:
																												# f = (d & b) | (not_32(d) & c)     # Alternate definition for f
																												__UpperCAmelCase   :						Optional[Any]      							=					c ^ (d & (b ^ c))
																												__UpperCAmelCase   :						List[Any]      							=					(5 * i + 1) % 1_6
																					elif i <= 4_7:
																												__UpperCAmelCase   :						int      							=					b ^ c ^ d
																												__UpperCAmelCase   :						List[str]      							=					(3 * i + 5) % 1_6
																					else:
																												__UpperCAmelCase   :						List[str]      							=					c ^ (b | not_aa(_UpperCamelCase							))
																												__UpperCAmelCase   :						Dict      							=					(7 * i) % 1_6
																					__UpperCAmelCase   :						Optional[Any]      							=					(f + a + added_consts[i] + block_words[g]) % 2**3_2
																					__UpperCAmelCase   :						Optional[Any]      							=					d
																					__UpperCAmelCase   :						Tuple      							=					c
																					__UpperCAmelCase   :						Dict      							=					b
																					__UpperCAmelCase   :						List[str]      							=					sum_aa(_UpperCamelCase       ,			left_rotate_aa(_UpperCamelCase       ,			shift_amounts[i]							)							)

														# Add hashed chunk to running total
														__UpperCAmelCase   :						Any      							=					sum_aa(_UpperCamelCase       ,			_UpperCamelCase							)
														__UpperCAmelCase   :						Tuple      							=					sum_aa(_UpperCamelCase       ,			_UpperCamelCase							)
														__UpperCAmelCase   :						List[str]      							=					sum_aa(_UpperCamelCase       ,			_UpperCamelCase							)
														__UpperCAmelCase   :						Optional[int]      							=					sum_aa(_UpperCamelCase       ,			_UpperCamelCase							)

							__UpperCAmelCase   :						Union[str, Any]      							=					reformat_hex(_UpperCamelCase							) + reformat_hex(_UpperCamelCase							) + reformat_hex(_UpperCamelCase							) + reformat_hex(_UpperCamelCase							)
							return digest


if __name__ == "__main__":
							import doctest

							doctest.testmod()




"""simple docstring"""






import math
def      lowerCamelCase       (     _UpperCamelCase		:      int							)		->       list[int]:

							'''simple docstring'''



							__UpperCAmelCase   :						List[Any]      							=					[]
							__UpperCAmelCase   :						Dict      							=					2
							__UpperCAmelCase   :						Union[str, Any]      							=					int(math.sqrt(_UpperCamelCase							)							)  # Size of every segment
							__UpperCAmelCase   :						Tuple      							=					[True] * (end + 1)
							__UpperCAmelCase   :						int      							=					[]

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

							__UpperCAmelCase   :						Optional[int]      							=					end + 1
							__UpperCAmelCase   :						Dict      							=					min(2 * end       ,			_UpperCamelCase							)

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

																					for j in range(_UpperCamelCase       ,			high + 1       ,			_UpperCamelCase							):
																												__UpperCAmelCase   :						Tuple      							=					False

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

														__UpperCAmelCase   :						Tuple      							=					high + 1
														__UpperCAmelCase   :						Optional[int]      							=					min(high + end       ,			_UpperCamelCase							)

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