





'''simple docstring'''





from collections.abc import Generator
from math import sin

def       A__(		__lowerCAmelCase ):


				if len(lowerCamelCase__ ) != 32:
								raise ValueError('Input must be of length 32' )

				_snake_case :			Dict  						=   b""
				for i in [3, 2, 1, 0]:
								little_endian += string_aa[8 * i : 8 * i + 8]
				return little_endian

def       A__(		__lowerCAmelCase ):


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

				_snake_case :			Dict  						=   format(lowerCamelCase__	,			'08x' )[-8:]
				_snake_case :			int  						=   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       A__(		__lowerCAmelCase ):
				_snake_case :			Tuple  						=   b""
				for char in message:
								bit_string += format(lowerCamelCase__	,			'08b' ).encode('utf-8' )
				_snake_case :			str  						=   format(len(lowerCamelCase__ )	,			'064b' ).encode('utf-8' )

				# Pad bit_string to a multiple of 512 chars
				bit_string += b"1"
				while len(lowerCamelCase__ ) % 5_12 != 4_48:
								bit_string += b"0"
				bit_string += to_little_endian(start_len[32:] ) + to_little_endian(start_len[:32] )

				return bit_string

def       A__(		__lowerCAmelCase ):


				if len(lowerCamelCase__ ) % 5_12 != 0:
								raise ValueError('Input must have length that\'s a multiple of 512' )

				for pos in range(0	,			len(lowerCamelCase__ )	,			5_12 ):
								_snake_case :			Dict  						=   bit_string[pos : pos + 5_12]
								_snake_case :			int  						=   []
								for i in range(0	,			5_12	,			32 ):
												block_words.append(int(to_little_endian(block[i : i + 32] )	,			2 ) )
								yield block_words

def       A__(		__lowerCAmelCase ):


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

				_snake_case :			Union[str, Any]  						=   format(lowerCamelCase__	,			'032b' )
				_snake_case :			Tuple  						=   ""
				for c in i_str:
								new_str += "1" if c == "0" else "0"
				return int(lowerCamelCase__	,			2 )

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase ):
				return (a + b) % 2**32

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase ):


				if i < 0:
								raise ValueError('Input must be non-negative' )
				if shift < 0:
								raise ValueError('Shift must be non-negative' )
				return ((i << shift) ^ (i >> (32 - shift))) % 2**32

def       A__(		__lowerCAmelCase ):
				_snake_case :			Any  						=   preprocess(lowerCamelCase__ )

				_snake_case :			List[Any]  						=   [int(2**32 * abs(sin(i + 1 ) ) ) for i in range(64 )]

				# Starting states
				_snake_case :			Tuple  						=   0X6745_2301
				_snake_case :			str  						=   0Xefcd_ab89
				_snake_case :			Dict  						=   0X98ba_dcfe
				_snake_case :			str  						=   0X1032_5476

				_snake_case :			Optional[Any]  						=   [
				    7,
				    12,
				    17,
				    22,
				    7,
				    12,
				    17,
				    22,
				    7,
				    12,
				    17,
				    22,
				    7,
				    12,
				    17,
				    22,
				    5,
				    9,
				    14,
				    20,
				    5,
				    9,
				    14,
				    20,
				    5,
				    9,
				    14,
				    20,
				    5,
				    9,
				    14,
				    20,
				    4,
				    11,
				    16,
				    23,
				    4,
				    11,
				    16,
				    23,
				    4,
				    11,
				    16,
				    23,
				    4,
				    11,
				    16,
				    23,
				    6,
				    10,
				    15,
				    21,
				    6,
				    10,
				    15,
				    21,
				    6,
				    10,
				    15,
				    21,
				    6,
				    10,
				    15,
				    21,
				]

				# Process bit string in chunks, each with 16 32-char words
				for block_words in get_block_words(lowerCamelCase__ ):
								_snake_case :			str  						=   aa
								_snake_case :			Optional[int]  						=   ba
								_snake_case :			Optional[int]  						=   ca
								_snake_case :			Tuple  						=   da

								# Hash current chunk
								for i in range(64 ):
												if i <= 15:
																# f = (b & c) | (not_32(b) & d)     # Alternate definition for f
																_snake_case :			Union[str, Any]  						=   d ^ (b & (c ^ d))
																_snake_case :			Tuple  						=   i
												elif i <= 31:
																# f = (d & b) | (not_32(d) & c)     # Alternate definition for f
																_snake_case :			Optional[int]  						=   c ^ (d & (b ^ c))
																_snake_case :			Tuple  						=   (5 * i + 1) % 16
												elif i <= 47:
																_snake_case :			str  						=   b ^ c ^ d
																_snake_case :			Union[str, Any]  						=   (3 * i + 5) % 16
												else:
																_snake_case :			str  						=   c ^ (b | not_aa(lowerCamelCase__ ))
																_snake_case :			Tuple  						=   (7 * i) % 16
												_snake_case :			Union[str, Any]  						=   (f + a + added_consts[i] + block_words[g]) % 2**32
												_snake_case :			Tuple  						=   d
												_snake_case :			Any  						=   c
												_snake_case :			str  						=   b
												_snake_case :			Any  						=   sum_aa(lowerCamelCase__	,			left_rotate_aa(lowerCamelCase__	,			shift_amounts[i] ) )

								# Add hashed chunk to running total
								_snake_case :			Dict  						=   sum_aa(lowerCamelCase__	,			lowerCamelCase__ )
								_snake_case :			Union[str, Any]  						=   sum_aa(lowerCamelCase__	,			lowerCamelCase__ )
								_snake_case :			Optional[Any]  						=   sum_aa(lowerCamelCase__	,			lowerCamelCase__ )
								_snake_case :			Optional[Any]  						=   sum_aa(lowerCamelCase__	,			lowerCamelCase__ )

				_snake_case :			List[str]  						=   reformat_hex(lowerCamelCase__ ) + reformat_hex(lowerCamelCase__ ) + reformat_hex(lowerCamelCase__ ) + reformat_hex(lowerCamelCase__ )
				return digest


if __name__ == "__main__":
		import doctest

		doctest.testmod()













import itertools
import math

def       A__(		__lowerCAmelCase ):

				if 1 < number < 4:
								# 2 and 3 are primes
								return True
				elif number < 2 or number % 2 == 0 or number % 3 == 0:
								# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
								return False

				# All primes number are in format of 6k +/- 1
				for i in range(5	,			int(math.sqrt(__lowerCAmelCase ) + 1 )	,			6 ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True

def       A__(		):
				_snake_case :			Optional[Any]  						=   2
				while True:
								if is_prime(__lowerCAmelCase ):
												yield num
								num += 1

def       A__(		__lowerCAmelCase = 1_00_01 ):
				return next(itertools.islice(prime_generator()	,			nth - 1	,			__lowerCAmelCase ) )


if __name__ == "__main__":
		print(F'''{solution() = }''')






