
from __future__ import annotations

from math import gcd



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__ = 2 ,			lowerCAmelCase__ = 1 ,			lowerCAmelCase__ = 3 ,			):
					'''simple docstring'''
					# A value less than 2 can cause an infinite loop in the algorithm.
					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(lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		) -> int:
										return (pow(lowerCAmelCase__ ,			2		) + step) % modulus

					for _ in range(lowerCAmelCase__		):
										# These track the position within the cycle detection logic.
										lowercase							=						seed
										lowercase							=						seed

										while True:
															# At each iteration, the tortoise moves one step and the hare moves two.
															lowercase							=						rand_fn(lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		)
															lowercase							=						rand_fn(lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		)
															lowercase							=						rand_fn(lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		)

															# 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							=						gcd(hare - tortoise ,			lowerCAmelCase__		)

															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							=						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

							lowercase__		:Union[str, Any]   =    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",
							)
							lowercase__		:Any   =    parser.parse_args()

							lowercase__		:str   =    pollard_rho(args.num, attempts=args.attempts)
							if divisor is None:
														print(F'{args.num} is probably prime')
							else:
														lowercase__		:Union[str, Any]   =    args.num // divisor
														print(F'{args.num} = {divisor} * {quotient}')






import unittest

from transformers import SPIECE_UNDERLINE, XLNetTokenizer, XLNetTokenizerFast
from transformers.testing_utils import get_tests_dir, require_sentencepiece, require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin


lowercase__		:List[Any]   =    get_tests_dir("fixtures/test_sentencepiece.model")







@require_sentencepiece
@require_tokenizers
class 				lowercase		(					SCREAMING_SNAKE_CASE__       ,  unittest.TestCase		):
							lowercase_       :       str       					=XLNetTokenizer
							lowercase_       :       Dict       					=XLNetTokenizerFast
							lowercase_       :       str       					=True
							lowercase_       :       str       					=True




							def  A__      (				self):
												super().setUp()

												# We have a SentencePiece fixture for testing
												lowercase							=						XLNetTokenizer(A__   ,keep_accents=A__)
												tokenizer.sanitize_special_tokens()
												tokenizer.save_pretrained(self.tmpdirname)




							def  A__      (				self):
												lowercase							=						'''<s>'''
												lowercase							=						1

												self.assertEqual(self.get_tokenizer()._convert_token_to_id(A__)   ,A__)
												self.assertEqual(self.get_tokenizer()._convert_id_to_token(A__)   ,A__)




							def  A__      (				self):
												lowercase							=						list(self.get_tokenizer().get_vocab().keys())

												self.assertEqual(vocab_keys[0]   ,'''<unk>''')
												self.assertEqual(vocab_keys[1]   ,'''<s>''')
												self.assertEqual(vocab_keys[-1]   ,'''<eod>''')
												self.assertEqual(len(A__)   ,1_0_0_6)




							def  A__      (				self):
												self.assertEqual(self.get_tokenizer().vocab_size   ,1_0_0_0)




							def  A__      (				self):
												lowercase							=						XLNetTokenizer(A__   ,keep_accents=A__)

												lowercase							=						tokenizer.tokenize('''This is a test''')
												self.assertListEqual(A__   ,['''▁This''', '''▁is''', '''▁a''', '''▁t''', '''est'''])

												self.assertListEqual(tokenizer.convert_tokens_to_ids(A__)   ,[2_8_5, 4_6, 1_0, 1_7_0, 3_8_2])

												lowercase							=						tokenizer.tokenize('''I was born in 92000, and this is falsé.''')
												self.assertListEqual(
												    A__   ,[
												        SPIECE_UNDERLINE + '''I''',
												        SPIECE_UNDERLINE + '''was''',
												        SPIECE_UNDERLINE + '''b''',
												        '''or''',
												        '''n''',
												        SPIECE_UNDERLINE + '''in''',
												        SPIECE_UNDERLINE + '''''',
												        '''9''',
												        '''2''',
												        '''0''',
												        '''0''',
												        '''0''',
												        ''',''',
												        SPIECE_UNDERLINE + '''and''',
												        SPIECE_UNDERLINE + '''this''',
												        SPIECE_UNDERLINE + '''is''',
												        SPIECE_UNDERLINE + '''f''',
												        '''al''',
												        '''s''',
												        '''é''',
												        '''.''',
												    ]   ,)
												lowercase							=						tokenizer.convert_tokens_to_ids(A__)
												self.assertListEqual(A__   ,[8, 2_1, 8_4, 5_5, 2_4, 1_9, 7, 0, 6_0_2, 3_4_7, 3_4_7, 3_4_7, 3, 1_2, 6_6, 4_6, 7_2, 8_0, 6, 0, 4])

												lowercase							=						tokenizer.convert_ids_to_tokens(A__)
												self.assertListEqual(
												    A__   ,[
												        SPIECE_UNDERLINE + '''I''',
												        SPIECE_UNDERLINE + '''was''',
												        SPIECE_UNDERLINE + '''b''',
												        '''or''',
												        '''n''',
												        SPIECE_UNDERLINE + '''in''',
												        SPIECE_UNDERLINE + '''''',
												        '''<unk>''',
												        '''2''',
												        '''0''',
												        '''0''',
												        '''0''',
												        ''',''',
												        SPIECE_UNDERLINE + '''and''',
												        SPIECE_UNDERLINE + '''this''',
												        SPIECE_UNDERLINE + '''is''',
												        SPIECE_UNDERLINE + '''f''',
												        '''al''',
												        '''s''',
												        '''<unk>''',
												        '''.''',
												    ]   ,)




							def  A__      (				self):
												lowercase							=						XLNetTokenizer(A__   ,do_lower_case=A__)
												lowercase							=						tokenizer.tokenize('''I was born in 92000, and this is falsé.''')
												self.assertListEqual(
												    A__   ,[
												        SPIECE_UNDERLINE + '''''',
												        '''i''',
												        SPIECE_UNDERLINE + '''was''',
												        SPIECE_UNDERLINE + '''b''',
												        '''or''',
												        '''n''',
												        SPIECE_UNDERLINE + '''in''',
												        SPIECE_UNDERLINE + '''''',
												        '''9''',
												        '''2''',
												        '''0''',
												        '''0''',
												        '''0''',
												        ''',''',
												        SPIECE_UNDERLINE + '''and''',
												        SPIECE_UNDERLINE + '''this''',
												        SPIECE_UNDERLINE + '''is''',
												        SPIECE_UNDERLINE + '''f''',
												        '''al''',
												        '''se''',
												        '''.''',
												    ]   ,)
												self.assertListEqual(tokenizer.tokenize('''H\u00E9llo''')   ,['''▁he''', '''ll''', '''o'''])




							def  A__      (				self):
												lowercase							=						XLNetTokenizer(A__   ,do_lower_case=A__)
												lowercase							=						tokenizer.tokenize('''I was born in 92000, and this is falsé.''')
												self.assertListEqual(
												    A__   ,[
												        SPIECE_UNDERLINE + '''I''',
												        SPIECE_UNDERLINE + '''was''',
												        SPIECE_UNDERLINE + '''b''',
												        '''or''',
												        '''n''',
												        SPIECE_UNDERLINE + '''in''',
												        SPIECE_UNDERLINE + '''''',
												        '''9''',
												        '''2''',
												        '''0''',
												        '''0''',
												        '''0''',
												        ''',''',
												        SPIECE_UNDERLINE + '''and''',
												        SPIECE_UNDERLINE + '''this''',
												        SPIECE_UNDERLINE + '''is''',
												        SPIECE_UNDERLINE + '''f''',
												        '''al''',
												        '''se''',
												        '''.''',
												    ]   ,)




							@slow
							def  A__      (				self):
												lowercase							=						XLNetTokenizer.from_pretrained('''xlnet-base-cased''')

												lowercase							=						tokenizer.encode('''sequence builders'''   ,add_special_tokens=A__)
												lowercase							=						tokenizer.encode('''multi-sequence build'''   ,add_special_tokens=A__)

												lowercase							=						tokenizer.build_inputs_with_special_tokens(A__)
												lowercase							=						tokenizer.build_inputs_with_special_tokens(A__   ,A__)

												assert encoded_sentence == text + [4, 3]
												assert encoded_pair == text + [4] + text_a + [4, 3]





							@slow
							def  A__      (				self):
												# fmt: off
												lowercase							=						{'''input_ids''': [[1_7, 2_1_4_4_2, 2_7_0, 1_7, 1_0, 1_4_6_4_5, 3_1_8, 3_4, 1_7, 4_5_4_6, 3_1_4_5, 7_8_7, 1_3, 7_7_5_2, 2_2_0_1_8, 2_3, 2_1, 1_7, 4_5_4_6, 3_1_4_5, 7_8_7, 1_3, 3_3_5_2, 1_4_4_3_1, 1_3, 5_5_0_0, 1_1, 1_1_7_6, 5_8_0, 1_3, 1_6_8_1_9, 4_7_9_7, 2_3, 1_7, 1_0, 1_7_1_3_5, 6_5_8, 1_9, 4_5_7, 7_9_3_2, 1_3, 1_8_4, 1_9, 3_1_5_4, 1_7_1_3_5, 6_4_6_8, 1_9, 1_4_0_4, 1_2_2_6_9, 1_9, 4_2_2_9, 5_3_5_6, 1_6_2_6_4, 4_6, 1_9, 1_7, 2_0_5_4_5, 1_0_3_9_5, 9, 9, 9, 1_1, 2_8, 6_4_2_1, 9_5_3_1, 2_0_7_2_9, 1_7, 1_0, 3_5_3, 1_7_0_2_2, 1_1, 2_1, 6_4_2_1, 9_5_3_1, 1_6_9_4_9, 1_7, 1_0, 1_1_5_0_9, 7_5_3, 1_1, 3_3, 9_5, 2_4_2_1, 7_3_8_5, 9_5_6, 1_4_4_3_1, 2_6_2_6, 2_5, 8_4_2, 7_3_8_5, 4_8_3_6, 2_1, 1_4_2_9, 2_2_7_2, 9_8_5_5, 3_1_2_0, 1_6_1, 2_4_7_3_8, 1_9, 1_3_2_0_3, 6_5_8, 2_1_8, 7_8_7, 2_1, 4_3_0, 1_8_4_8_2, 8_4_7, 2_6_3_7, 9, 4, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3_2_2, 2_2_1_7_8, 2_7, 1_0_6_4, 2_2, 9_5_6, 1_3, 1_1_1_0_1, 1_4_2_9, 5_8_5_4, 2_4_3_1_3, 1_8_9_5_3, 4_0, 4_2_2, 2_4_3_6_6, 6_8, 1_7_5_8, 3_7, 1_0_4_8_3, 1_4_2_5_7, 3_1, 2_0_7, 2_6_3, 2_1, 2_0_3, 3_7_7_3, 2_5, 7_1, 9_7_3_5, 9, 4, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3_2, 2_0_4_9, 3_4_4_2, 1_7, 1_3_8_9_4, 3_3_8_0, 2_3, 9_5, 1_8, 1_7_6_3_4, 2_2_8_8, 9, 4, 3]], '''token_type_ids''': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]], '''attention_mask''': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}  # noqa: E501
												# fmt: on

												self.tokenizer_integration_test_util(
												    expected_encoding=A__   ,model_name='''xlnet-base-cased'''   ,revision='''c841166438c31ec7ca9a106dee7bb312b73ae511'''   ,)




