
from math import sqrt







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    bool:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (
           number >= 0
       ), "'number' must been an int and positive"

       lowercase							:     Union[str, Any]       	=      True

       # 0 and 1 are none primes.
       if number <= 1:
              lowercase							:     str       	=      False

       for divisor in range(2					,	int(round(sqrt(SCREAMING_SNAKE_CASE__				)				)				) + 1				):
              # if 'number' divisible by 'divisor' then sets 'status'
              # of false and break up the loop.
              if number % divisor == 0:
                     lowercase							:     Any       	=      False
                     break

    # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'status' must been from type bool"

       return status







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Union[str, Any]:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (n > 2), "'N' must been an int and > 2"

       # beginList: contains all natural numbers from 2 up to N
       lowercase							:     str       	=      list(range(2					,	n + 1				)				)

       lowercase							:     Tuple       	=      []  # this list will be returns.

       # actual sieve of erathostenes
       for i in range(len(SCREAMING_SNAKE_CASE__				)				):
              for j in range(i + 1					,	len(SCREAMING_SNAKE_CASE__				)				):
                     if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
                            lowercase							:     Tuple       	=      0

    # filters actual prime numbers.
       lowercase							:     int       	=      [x for x in begin_list if x != 0]

       # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'ans' must been from type list"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Optional[Any]:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (n > 2), "'N' must been an int and > 2"

       lowercase							:     Dict       	=      []

       # iterates over all numbers between 2 up to N+1
       # if a number is prime then appends to list 'ans'
       for number in range(2					,	n + 1				):
              if is_prime(SCREAMING_SNAKE_CASE__				):
                     ans.append(SCREAMING_SNAKE_CASE__				)

    # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'ans' must been from type list"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Tuple:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and number >= 0, "'number' must been an int and >= 0"

       lowercase							:     Tuple       	=      []  # this list will be returns of the function.

       # potential prime number factors.

       lowercase							:     Optional[Any]       	=      2

       lowercase							:     Any       	=      number

       if number == 0 or number == 1:
              ans.append(SCREAMING_SNAKE_CASE__				)

       # if 'number' not prime then builds the prime factorization of 'number'
       elif not is_prime(SCREAMING_SNAKE_CASE__				):
              while quotient != 1:
                     if is_prime(SCREAMING_SNAKE_CASE__				) and (quotient % factor == 0):
                            ans.append(SCREAMING_SNAKE_CASE__				)
                            quotient /= factor
                     else:
                            factor += 1

       else:
              ans.append(SCREAMING_SNAKE_CASE__				)

       # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'ans' must been from type list"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    List[Any]:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (
           number >= 0
       ), "'number' bust been an int and >= 0"

       lowercase							:     Tuple       	=      0

       # prime factorization of 'number'
       lowercase							:     Optional[int]       	=      prime_factorization(SCREAMING_SNAKE_CASE__				)

       lowercase							:     Union[str, Any]       	=      max(SCREAMING_SNAKE_CASE__				)

       # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'ans' must been from type int"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    str:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (
           number >= 0
       ), "'number' bust been an int and >= 0"

       lowercase							:     Union[str, Any]       	=      0

       # prime factorization of 'number'
       lowercase							:     Tuple       	=      prime_factorization(SCREAMING_SNAKE_CASE__				)

       lowercase							:     Union[str, Any]       	=      min(SCREAMING_SNAKE_CASE__				)

       # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'ans' must been from type int"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Optional[Any]:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'number' must been an int"
       assert isinstance(number % 2 == 0					,	SCREAMING_SNAKE_CASE__				), "compare bust been from type bool"

       return number % 2 == 0







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    int:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				), "'number' must been an int"
       assert isinstance(number % 2 != 0					,	SCREAMING_SNAKE_CASE__				), "compare bust been from type bool"

       return number % 2 != 0







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    int:
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (number > 2) and is_even(SCREAMING_SNAKE_CASE__				)
       ), "'number' must been an int, even and > 2"

       lowercase							:     Union[str, Any]       	=      []  # this list will returned

       # creates a list of prime numbers between 2 up to 'number'
       lowercase							:     str       	=      get_prime_numbers(SCREAMING_SNAKE_CASE__				)
       lowercase							:     Any       	=      len(SCREAMING_SNAKE_CASE__				)

       # run variable for while-loops.
       lowercase							:     Optional[Any]       	=      0
       lowercase							:     List[Any]       	=      None

       # exit variable. for break up the loops
       lowercase							:     Any       	=      True

       while i < len_pn and loop:
              lowercase							:     str       	=      i + 1

              while j < len_pn and loop:
                     if prime_numbers[i] + prime_numbers[j] == number:
                            lowercase							:     Union[str, Any]       	=      False
                            ans.append(prime_numbers[i]				)
                            ans.append(prime_numbers[j]				)

                     j += 1

              i += 1

       # precondition
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and (len(SCREAMING_SNAKE_CASE__				) == 2)
           and (ans[0] + ans[1] == number)
           and is_prime(ans[0]				)
           and is_prime(ans[1]				)
       ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) ->    str:
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and (numbera >= 0)
           and (numbera >= 0)
       ), "'number1' and 'number2' must been positive integer."

       lowercase							:     Union[str, Any]       	=      0

       while numbera != 0:
              lowercase							:     Optional[int]       	=      numbera % numbera
              lowercase							:     Optional[int]       	=      numbera
              lowercase							:     Dict       	=      rest

       # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (
           numbera >= 0
       ), "'number' must been from type int and positive"

       return numbera







def 						_snake_case(  SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) ->    Tuple:
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and (numbera >= 1)
           and (numbera >= 1)
       ), "'number1' and 'number2' must been positive integer."

       lowercase							:     Dict       	=      1  # actual answer that will be return.

       # for kgV (x,1)
       if numbera > 1 and numbera > 1:
              # builds the prime factorization of 'number1' and 'number2'
              lowercase							:     Optional[Any]       	=      prime_factorization(SCREAMING_SNAKE_CASE__				)
              lowercase							:     Optional[int]       	=      prime_factorization(SCREAMING_SNAKE_CASE__				)

       elif numbera == 1 or numbera == 1:
              lowercase							:     Union[str, Any]       	=      []
              lowercase							:     List[str]       	=      []
              lowercase							:     Dict       	=      max(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)

       lowercase							:     Union[str, Any]       	=      0
       lowercase							:     Optional[Any]       	=      0

       lowercase							:     List[str]       	=      []  # captured numbers int both 'primeFac1' and 'primeFac2'

       # iterates through primeFac1
       for n in prime_fac_a:
              if n not in done:
                     if n in prime_fac_a:
                            lowercase							:     Dict       	=      prime_fac_a.count(SCREAMING_SNAKE_CASE__				)
                            lowercase							:     Optional[Any]       	=      prime_fac_a.count(SCREAMING_SNAKE_CASE__				)

                            for _ in range(max(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)				):
                                   ans *= n

                     else:
                            lowercase							:     List[Any]       	=      prime_fac_a.count(SCREAMING_SNAKE_CASE__				)

                            for _ in range(SCREAMING_SNAKE_CASE__				):
                                   ans *= n

                     done.append(SCREAMING_SNAKE_CASE__				)

    # iterates through primeFac2
       for n in prime_fac_a:
              if n not in done:
                     lowercase							:     Optional[int]       	=      prime_fac_a.count(SCREAMING_SNAKE_CASE__				)

                     for _ in range(SCREAMING_SNAKE_CASE__				):
                            ans *= n

                     done.append(SCREAMING_SNAKE_CASE__				)

    # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (
           ans >= 0
       ), "'ans' must been from type int and positive"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Any:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (n >= 0), "'number' must been a positive int"

       lowercase							:     Dict       	=      0
       lowercase							:     List[str]       	=      2  # this variable holds the answer

       while index < n:
              index += 1

              ans += 1  # counts to the next number

              # if ans not prime then
              # runs to the next prime number.
              while not is_prime(SCREAMING_SNAKE_CASE__				):
                     ans += 1

    # precondition
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and is_prime(
           SCREAMING_SNAKE_CASE__				), "'ans' must been a prime number and from type int"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) ->    List[Any]:
       assert (
           is_prime(SCREAMING_SNAKE_CASE__				) and is_prime(SCREAMING_SNAKE_CASE__				) and (p_number_a < p_number_a)
       ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

       lowercase							:     List[str]       	=      p_number_a + 1  # jump to the next number

       lowercase							:     List[Any]       	=      []  # this list will be returns.

       # if number is not prime then
       # fetch the next prime number.
       while not is_prime(SCREAMING_SNAKE_CASE__				):
              number += 1

       while number < p_number_a:
              ans.append(SCREAMING_SNAKE_CASE__				)

              number += 1

              # fetch the next prime number.
              while not is_prime(SCREAMING_SNAKE_CASE__				):
                     number += 1

    # precondition
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and ans[0] != p_number_a
           and ans[len(SCREAMING_SNAKE_CASE__				) - 1] != p_number_a
       ), "'ans' must been a list without the arguments"

       # 'ans' contains not 'pNumber1' and 'pNumber2' !
       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Any:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (n >= 1), "'n' must been int and >= 1"

       lowercase							:     Optional[Any]       	=      []  # will be returned.

       for divisor in range(1					,	n + 1				):
              if n % divisor == 0:
                     ans.append(SCREAMING_SNAKE_CASE__				)

    # precondition
       assert ans[0] == 1 and ans[len(SCREAMING_SNAKE_CASE__				) - 1] == n, "Error in function getDivisiors(...)"

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Any:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (
           number > 1
       ), "'number' must been an int and >= 1"

       lowercase							:     str       	=      get_divisors(SCREAMING_SNAKE_CASE__				)

       # precondition
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and (divisors[0] == 1)
           and (divisors[len(SCREAMING_SNAKE_CASE__				) - 1] == number)
       ), "Error in help-function getDivisiors(...)"

       # summed all divisors up to 'number' (exclusive), hence [:-1]
       return sum(divisors[:-1]				) == number







def 						_snake_case(  SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) ->    Dict:
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and (denominator != 0)
       ), "The arguments must been from type int and 'denominator' != 0"

       # build the greatest common divisor of numerator and denominator.
       lowercase							:     Tuple       	=      gcd(abs(SCREAMING_SNAKE_CASE__				)					,	abs(SCREAMING_SNAKE_CASE__				)				)

       # precondition
       assert (
           isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)
           and (numerator % gcd_of_fraction == 0)
           and (denominator % gcd_of_fraction == 0)
       ), "Error in function gcd(...,...)"

       return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    int:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (n >= 0), "'n' must been a int and >= 0"

       lowercase							:     List[str]       	=      1  # this will be return.

       for factor in range(1					,	n + 1				):
              ans *= factor

       return ans







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Union[str, Any]:
       assert isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) and (n >= 0), "'n' must been an int and >= 0"

       lowercase							:     int       	=      0
       lowercase							:     Union[str, Any]       	=      1
       lowercase							:     int       	=      1  # this will be return

       for _ in range(n - 1				):
              lowercase							:     Optional[int]       	=      ans
              ans += fiba
              lowercase							:     Optional[int]       	=      tmp

       return ans


'''simple docstring'''







import inspect
import os
import unittest
from pathlib import Path

import torch

import accelerate
from accelerate.test_utils import execute_subprocess_async
from accelerate.test_utils.testing import run_command







class UpperCAmelCase__	( unittest.TestCase	):





  """simple docstring"""

  __UpperCAmelCase				:				Optional[Any]   =					inspect.getfile(accelerate.test_utils	)
  __UpperCAmelCase				:				List[str]   =					os.path.sep.join(mod_file.split(os.path.sep	)[:-1] + ['''scripts''', '''test_cli.py''']	)

  __UpperCAmelCase				:				Dict   =					['''accelerate''', '''launch''']
  __UpperCAmelCase				:				Dict   =					Path.home() / '''.cache/huggingface/accelerate'''
  __UpperCAmelCase				:				Dict   =					'''default_config.yaml'''
  __UpperCAmelCase				:				Optional[Any]   =					config_folder / config_file
  __UpperCAmelCase				:				Dict   =					config_folder / '''_default_config.yaml'''

  __UpperCAmelCase				:				Any   =					Path('''tests/test_configs'''	)


  @classmethod
  def   __lowercase		(		cls      :     int       ):


     '''simple docstring'''






     if cls.config_path.is_file():
        cls.config_path.rename(cls.changed_path       )


  @classmethod
  def   __lowercase		(		cls      :     List[Any]       ):


     '''simple docstring'''






     if cls.changed_path.is_file():
        cls.changed_path.rename(cls.config_path       )


  def   __lowercase		(		self      :     Optional[int]       ):


     '''simple docstring'''






     _a				:	Dict			=   self.base_cmd
     if torch.cuda.is_available() and (torch.cuda.device_count() > 1):
        cmd += ["--multi_gpu"]
     execute_subprocess_async(cmd + [self.test_file_path]							,env=os.environ.copy()       )


  def   __lowercase		(		self      :     Optional[Any]       ):


     '''simple docstring'''






     for config in sorted(self.test_config_path.glob('**/*.yaml'       )       ):
        with self.subTest(config_file=_a       ):
           execute_subprocess_async(
               self.base_cmd + ['--config_file', str(_a       ), self.test_file_path]							,env=os.environ.copy()       )


  def   __lowercase		(		self      :     Optional[int]       ):


     '''simple docstring'''






     execute_subprocess_async(['accelerate', 'test']							,env=os.environ.copy()       )







class UpperCAmelCase__	( unittest.TestCase	):





  """simple docstring"""

  __UpperCAmelCase				:				Optional[Any]   =					'''test-tpu'''
  __UpperCAmelCase				:				Any   =					'''us-central1-a'''
  __UpperCAmelCase				:				List[Any]   =					'''ls'''
  __UpperCAmelCase				:				Any   =					['''accelerate''', '''tpu-config''']
  __UpperCAmelCase				:				Dict   =					'''cd /usr/share'''
  __UpperCAmelCase				:				Any   =					'''tests/test_samples/test_command_file.sh'''
  __UpperCAmelCase				:				List[Any]   =					'''Running gcloud compute tpus tpu-vm ssh'''


  def   __lowercase		(		self      :     Dict       ):


     '''simple docstring'''






     _a				:	Optional[Any]			=   run_command(
         self.cmd
         + ['--command', self.command, '--tpu_zone', self.tpu_zone, '--tpu_name', self.tpu_name, '--debug']							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; ls --worker all"""							,_a							,)


  def   __lowercase		(		self      :     List[str]       ):


     '''simple docstring'''






     _a				:	Any			=   run_command(
         self.cmd
         + [
             '--config_file',
             'tests/test_configs/0_12_0.yaml',
             '--command',
             self.command,
             '--tpu_zone',
             self.tpu_zone,
             '--tpu_name',
             self.tpu_name,
             '--debug',
         ]							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; ls --worker all"""							,_a							,)


  def   __lowercase		(		self      :     List[str]       ):


     '''simple docstring'''






     _a				:	Optional[int]			=   run_command(
         self.cmd + ['--config_file', 'tests/test_configs/latest.yaml', '--debug']							,return_stdout=_a       )
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; echo \"hello world\"; echo \"this is a second command\" --worker all"""							,_a							,)


  def   __lowercase		(		self      :     int       ):


     '''simple docstring'''






     _a				:	Optional[Any]			=   run_command(
         self.cmd + ['--config_file', 'tests/test_configs/latest.yaml', '--command', self.command, '--debug']							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; ls --worker all"""							,_a							,)


  def   __lowercase		(		self      :     str       ):


     '''simple docstring'''






     _a				:	List[str]			=   run_command(
         self.cmd
         + [
             '--config_file',
             'tests/test_configs/latest.yaml',
             '--command',
             self.command,
             '--command',
             'echo "Hello World"',
             '--debug',
         ]							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; ls; echo \"Hello World\" --worker all"""							,_a							,)


  def   __lowercase		(		self      :     Union[str, Any]       ):


     '''simple docstring'''






     _a				:	Any			=   run_command(
         self.cmd
         + ['--config_file', 'tests/test_configs/latest.yaml', '--command_file', self.command_file, '--debug']							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; echo \"hello world\"; echo \"this is a second command\" --worker all"""							,_a							,)


  def   __lowercase		(		self      :     Union[str, Any]       ):


     '''simple docstring'''






     _a				:	Union[str, Any]			=   run_command(
         self.cmd
         + [
             '--config_file',
             'tests/test_configs/0_12_0.yaml',
             '--command_file',
             self.command_file,
             '--tpu_zone',
             self.tpu_zone,
             '--tpu_name',
             self.tpu_name,
             '--debug',
         ]							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; echo \"hello world\"; echo \"this is a second command\" --worker all"""							,_a							,)


  def   __lowercase		(		self      :     Any       ):


     '''simple docstring'''






     _a				:	Optional[int]			=   run_command(
         self.cmd + ['--config_file', 'tests/test_configs/latest.yaml', '--install_accelerate', '--debug']							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; pip install accelerate -U; echo \"hello world\"; echo \"this is a second command\" --worker all"""							,_a							,)


  def   __lowercase		(		self      :     List[str]       ):


     '''simple docstring'''






     _a				:	Optional[int]			=   run_command(
         self.cmd
         + [
             '--config_file',
             'tests/test_configs/latest.yaml',
             '--install_accelerate',
             '--accelerate_version',
             '12.0.0',
             '--debug',
         ]							,return_stdout=_a							,)
     self.assertIn(
         F"""{self.gcloud} test-tpu --zone us-central1-a --command {self.base_output}; pip install accelerate==12.0.0; echo \"hello world\"; echo \"this is a second command\" --worker all"""							,_a							,)



