
import random


def     __lowerCAmelCase			(			a__  )       ->  bool:
				__a										=    num - 1
				__a										=    0

				while s % 2 == 0:
								__a										=    s // 2
								t += 1

				for _ in range(5  ):
								__a										=    random.randrange(2						,    num - 1  )
								__a										=    pow(a__						,    a__						,    a__  )
								if v != 1:
												__a										=    0
												while v != (num - 1):
																if i == t - 1:
																				return False
																else:
																				__a										=    i + 1
																				__a										=    (v**2) % num
				return True


def     __lowerCAmelCase			(			a__  )       ->  bool:
				if num < 2:
								return False

				__a										=    [
				    2,
				    3,
				    5,
				    7,
				    11,
				    13,
				    17,
				    19,
				    23,
				    29,
				    31,
				    37,
				    41,
				    43,
				    47,
				    53,
				    59,
				    61,
				    67,
				    71,
				    73,
				    79,
				    83,
				    89,
				    97,
				    101,
				    103,
				    107,
				    109,
				    113,
				    127,
				    131,
				    137,
				    139,
				    149,
				    151,
				    157,
				    163,
				    167,
				    173,
				    179,
				    181,
				    191,
				    193,
				    197,
				    199,
				    211,
				    223,
				    227,
				    229,
				    233,
				    239,
				    241,
				    251,
				    257,
				    263,
				    269,
				    271,
				    277,
				    281,
				    283,
				    293,
				    307,
				    311,
				    313,
				    317,
				    331,
				    337,
				    347,
				    349,
				    353,
				    359,
				    367,
				    373,
				    379,
				    383,
				    389,
				    397,
				    401,
				    409,
				    419,
				    421,
				    431,
				    433,
				    439,
				    443,
				    449,
				    457,
				    461,
				    463,
				    467,
				    479,
				    487,
				    491,
				    499,
				    503,
				    509,
				    521,
				    523,
				    541,
				    547,
				    557,
				    563,
				    569,
				    571,
				    577,
				    587,
				    593,
				    599,
				    601,
				    607,
				    613,
				    617,
				    619,
				    631,
				    641,
				    643,
				    647,
				    653,
				    659,
				    661,
				    673,
				    677,
				    683,
				    691,
				    701,
				    709,
				    719,
				    727,
				    733,
				    739,
				    743,
				    751,
				    757,
				    761,
				    769,
				    773,
				    787,
				    797,
				    809,
				    811,
				    821,
				    823,
				    827,
				    829,
				    839,
				    853,
				    857,
				    859,
				    863,
				    877,
				    881,
				    883,
				    887,
				    907,
				    911,
				    919,
				    929,
				    937,
				    941,
				    947,
				    953,
				    967,
				    971,
				    977,
				    983,
				    991,
				    997,
				]

				if num in low_primes:
								return True

				for prime in low_primes:
								if (num % prime) == 0:
												return False

				return rabin_miller(a__  )


def     __lowerCAmelCase			(			a__ = 1024  )       ->  int:
				while True:
								__a										=    random.randrange(2 ** (keysize - 1)						,    2 ** (keysize)  )
								if is_prime_low_num(a__  ):
												return num


if __name__ == "__main__":
					A     :	Any    = generate_large_prime()
					print(('Prime number:', num))
					print(('is_prime_low_num:', is_prime_low_num(num)))

# XXX: we want transformers master here - in the absense of conftest manipulating sys.path:
# hack it in for now:
import sys
from pathlib import Path


A     :	Optional[Any]    = Path(__file__).resolve().parents[3] / 'src'
sys.path.insert(1, str(git_repo_path))

import dataclasses  # noqa
import io  # noqa
import itertools  # noqa
import json  # noqa
import os  # noqa
import unittest  # noqa
from copy import deepcopy  # noqa

from parameterized import parameterized  # noqa
from transformers import TrainingArguments, is_torch_available  # noqa
from transformers.deepspeed import is_deepspeed_available  # noqa
from transformers.file_utils import WEIGHTS_NAME  # noqa
from transformers.testing_utils import (  # noqa
    CaptureLogger,
    ExtendSysPath,
    TestCasePlus,
    execute_subprocess_async,
    get_gpu_count,
    mockenv_context,
    require_deepspeed,
    require_torch_gpu,
    require_torch_multi_gpu,
    slow,
)
from transformers.trainer_utils import set_seed  # noqa


set_seed(4_2)

A     :	List[str]    = {'base': 'patrickvonplaten/wav2vec2_tiny_random', 'robust': 'patrickvonplaten/wav2vec2_tiny_random_robust'}

A     :	Optional[int]    = 'zero2'
A     :	str    = 'zero3'
A     :	Tuple    = [ZEROa, ZEROa]


def     __lowerCAmelCase			(			a__						,    a__						,    a__  )       ->  Tuple:
				# customize the test name generator function as we want both params to appear in the sub-test
				# name, as by default it shows only the first param
				__a										=    parameterized.to_safe_name('''_'''.join(str(a__  ) for x in param.args  )  )
				return F"""{func.__name__}_{param_based_name}"""


# Cartesian-product of zero stages with models to test
A     :	Union[str, Any]    = list(itertools.product(stages, models.keys()))







@slow
@require_deepspeed
@require_torch_gpu
class 			__A( a			):




				@parameterized.expand(_snake_case		,     name_func=_snake_case				)
				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      Any:


								'''simple docstring'''




								self.run_and_check(
								    stage=_snake_case		,     model=_snake_case		,     distributed=_snake_case		,     fpaa=_snake_case		,     )




				@require_torch_multi_gpu
				@parameterized.expand(_snake_case		,     name_func=_snake_case				)
				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      int:


								'''simple docstring'''




								self.run_and_check(
								    stage=_snake_case		,     model=_snake_case		,     distributed=_snake_case		,     fpaa=_snake_case		,     )




				@parameterized.expand(_snake_case		,     name_func=_snake_case				)
				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      str:


								'''simple docstring'''




								self.run_and_check(
								    stage=_snake_case		,     model=_snake_case		,     distributed=_snake_case		,     fpaa=_snake_case		,     )




				@require_torch_multi_gpu
				@parameterized.expand(_snake_case		,     name_func=_snake_case				)
				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      Optional[Any]:


								'''simple docstring'''




								self.run_and_check(
								    stage=_snake_case		,     model=_snake_case		,     distributed=_snake_case		,     fpaa=_snake_case		,     )




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      Tuple:


								'''simple docstring'''




								pass




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case		,     _snake_case = 10		,     _snake_case = True		,     _snake_case = True		,     _snake_case = True		,     )    ->      Any:


								'''simple docstring'''




								__a										=    models[model]

								__a										=    self.run_trainer(
								    stage=_snake_case		,     model_name=_snake_case		,     eval_steps=_snake_case		,     num_train_epochs=1		,     distributed=_snake_case		,     fpaa=_snake_case		,     )

								self.do_checks(_snake_case				)

								return output_dir




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case		,     _snake_case = 10		,     _snake_case = 1		,     _snake_case = True		,     _snake_case = True		,     )    ->      Union[str, Any]:


								'''simple docstring'''




								__a										=    self.get_auto_remove_tmp_dir('''./xxx'''		,     after=_snake_case				)
								__a										=    F"""
            --model_name_or_path {model_name}
            --dataset_name hf-internal-testing/librispeech_asr_dummy
            --dataset_config_name clean
            --train_split_name validation
            --validation_split_name validation
            --output_dir {output_dir}
            --num_train_epochs {str(_snake_case				)}
            --per_device_train_batch_size 2
            --per_device_eval_batch_size 2
            --evaluation_strategy steps
            --learning_rate 5e-4
            --warmup_steps 8
            --orthography timit
            --preprocessing_num_workers 1
            --group_by_length
            --freeze_feature_extractor
            --report_to none
            --save_steps 0
            --eval_steps {eval_steps}
            --report_to none
        """.split()

								if fpaa:
												args.extend(['''--fp16''']				)

								# currently ds_config_wav2vec2_zero.json requires "zero_optimization.find_unused_parameters": true,
								# hence the separate config files
								__a										=    F"""--deepspeed {self.test_file_dir_str}/ds_config_wav2vec2_{stage}.json""".split()
								__a										=    [F"""{self.examples_dir_str}/research_projects/wav2vec2/run_asr.py"""]
								__a										=    self.get_launcher(_snake_case				)

								__a										=    launcher + script + args + ds_args
								# keep for quick debug
								# print(" ".join([f"\nPYTHONPATH={self.src_dir_str}"] +cmd)); die
								execute_subprocess_async(_snake_case		,     env=self.get_env()				)

								return output_dir




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case=False				)    ->      List[str]:


								'''simple docstring'''




								__a										=    min(2		,     get_gpu_count()				) if distributed else 1
								return F"""deepspeed --num_nodes 1 --num_gpus {num_gpus}""".split()