



import json
from typing import Iterator, List, Union

from tokenizers import AddedToken, Regex, Tokenizer, decoders, normalizers, pre_tokenizers, trainers
from tokenizers.implementations.base_tokenizer import BaseTokenizer
from tokenizers.models import Unigram
from tokenizers.processors import TemplateProcessing
class 					__A       (			lowerCamelCase__   ):





			def __init__(self				,     __magic_name__ = "▁"				,     __magic_name__ = True				,     __magic_name__ = "<unk>"				,     __magic_name__ = "</s>"				,     __magic_name__ = "<pad>"				,     ):
						lowerCamelCase__			:   Optional[int]										=		{
						    """pad""": {"""id""": 0, """token""": pad_token},
						    """eos""": {"""id""": 1, """token""": eos_token},
						    """unk""": {"""id""": 2, """token""": unk_token},
						}

						lowerCamelCase__			:   List[str]										=		[None] * len(self.special_tokens					)
						for token_dict in self.special_tokens.values():
									lowerCamelCase__			:   Union[str, Any]										=		token_dict["""token"""]

						lowerCamelCase__			:   Optional[int]										=		Tokenizer(Unigram()					)

						lowerCamelCase__			:   List[str]										=		normalizers.Sequence(
						    [
						        normalizers.Nmt(),
						        normalizers.NFKC(),
						        normalizers.Replace(Regex(""" {2,}"""					)				,     """ """					),
						        normalizers.Lowercase(),
						    ]					)
						lowerCamelCase__			:   Any										=		pre_tokenizers.Sequence(
						    [
						        pre_tokenizers.Metaspace(replacement=snake_case__				,     add_prefix_space=snake_case__					),
						        pre_tokenizers.Digits(individual_digits=snake_case__					),
						        pre_tokenizers.Punctuation(),
						    ]					)
						lowerCamelCase__			:   str										=		decoders.Metaspace(replacement=snake_case__				,     add_prefix_space=snake_case__					)

						lowerCamelCase__			:   Tuple										=		TemplateProcessing(
						    single=f"$A {self.special_tokens['eos']['token']}"				,     special_tokens=[(self.special_tokens["""eos"""]["""token"""], self.special_tokens["""eos"""]["""id"""])]				,     )

						lowerCamelCase__			:   Dict										=		{
						    """model""": """SentencePieceUnigram""",
						    """replacement""": replacement,
						    """add_prefix_space""": add_prefix_space,
						}

						super().__init__(snake_case__				,     snake_case__					)





			def 							_snake_case     (self				,     __magic_name__				,     __magic_name__ = 8000				,     __magic_name__ = True				,     ):
						lowerCamelCase__			:   List[str]										=		trainers.UnigramTrainer(
						    vocab_size=snake_case__				,     special_tokens=self.special_tokens_list				,     show_progress=snake_case__				,     )

						if isinstance(snake_case__				,     snake_case__					):
									lowerCamelCase__			:   Any										=		[files]
						self._tokenizer.train(snake_case__				,     trainer=snake_case__					)

						self.add_unk_id()





			def 							_snake_case     (self				,     __magic_name__				,     __magic_name__ = 8000				,     __magic_name__ = True				,     ):
						lowerCamelCase__			:   str										=		trainers.UnigramTrainer(
						    vocab_size=snake_case__				,     special_tokens=self.special_tokens_list				,     show_progress=snake_case__				,     )

						self._tokenizer.train_from_iterator(snake_case__				,     trainer=snake_case__					)

						self.add_unk_id()





			def 							_snake_case     (self					):
						lowerCamelCase__			:   str										=		json.loads(self._tokenizer.to_str()					)

						lowerCamelCase__			:   Union[str, Any]										=		self.special_tokens["""unk"""]["""id"""]

						lowerCamelCase__			:   Dict										=		Tokenizer.from_str(json.dumps(snake_case__					)					)










from __future__ import annotations

from math import gcd





def  __magic_name__  (				lowercase				,       lowercase = 2				,       lowercase = 1				,       lowercase = 3				,       )				-> int | None:

							"""simple docstring"""



							if num < 2:
														raise ValueError("""The input value cannot be less than 2"""				)

							# Because of the relationship between ``f(f(x))`` and ``f(x)``, this
							# algorithm struggles to find factors that are divisible by two.
							# As a workaround, we specifically check for two and even inputs.
							#   See: https://math.stackexchange.com/a/2856214/165820
							if num > 2 and num % 2 == 0:
														return 2

							# Pollard's Rho algorithm requires a function that returns pseudorandom
							# values between 0 <= X < ``num``.  It doesn't need to be random in the
							# sense that the output value is cryptographically secure or difficult
							# to calculate, it only needs to be random in the sense that all output
							# values should be equally likely to appear.
							# For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
							# However, the success of Pollard's algorithm isn't guaranteed and is
							# determined in part by the initial seed and the chosen random function.
							# To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
							# where ``C`` is a value that we can modify between each attempt.
							def rand_fn(lowercase				,       lowercase				,       lowercase				) -> int:
														return (pow(lowercase				,       2				) + step) % modulus

							for _ in range(lowercase				):
														# These track the position within the cycle detection logic.
														lowercase_	:   List[Any]  				=     seed
														lowercase_	:   Any  				=     seed

														while True:
																					# At each iteration, the tortoise moves one step and the hare moves two.
																					lowercase_	:   List[str]  				=     rand_fn(lowercase				,       lowercase				,       lowercase				)
																					lowercase_	:   str  				=     rand_fn(lowercase				,       lowercase				,       lowercase				)
																					lowercase_	:   Any  				=     rand_fn(lowercase				,       lowercase				,       lowercase				)

																					# At some point both the tortoise and the hare will enter a cycle whose
																					# length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
																					# the tortoise and hare will end up on the same value modulo ``p``.
																					# We can detect when this happens because the position difference between
																					# the tortoise and the hare will share a common divisor with ``num``.
																					lowercase_	:   Tuple  				=     gcd(hare - tortoise				,       lowercase				)

																					if divisor == 1:
																												# No common divisor yet, just keep searching.
																												continue
																					else:
																												# We found a common divisor!
																												if divisor == num:
																																			# Unfortunately, the divisor is ``num`` itself and is useless.
																																			break
																												else:
																																			# The divisor is a nontrivial factor of ``num``!
																																			return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
														lowercase_	:   int  				=     hare

														# The new step value for the random function can just be incremented.
														# At first the results will be similar to what the old function would
														# have produced, but the value will quickly diverge after a bit.
														step += 1

							# We haven't found a divisor within the requested number of attempts.
							# We were unlucky or ``num`` itself is actually prime.
							return None


if __name__ == "__main__":
							import argparse

							UpperCAmelCase_							=				argparse.ArgumentParser()
							parser.add_argument(
							    """num""",
							    type=int,
							    help="""The value to find a divisor of""",
							)
							parser.add_argument(
							    """--attempts""",
							    type=int,
							    default=3,
							    help="""The number of attempts before giving up""",
							)
							UpperCAmelCase_							=				parser.parse_args()

							UpperCAmelCase_							=				pollard_rho(args.num, attempts=args.attempts)
							if divisor is None:
														print(F'''{args.num} is probably prime''')
							else:
														UpperCAmelCase_							=				args.num // divisor
														print(F'''{args.num} = {divisor} * {quotient}''')