



from math import sqrt
def        lowercase_							(A : int      ):
       assert isinstance(A		,					A      ) and (
           number >= 0
       ), "'number' must been an int and positive"

       snake_case__							:	Optional[Any]   	=	True

       # 0 and 1 are none primes.
       if number <= 1:
              snake_case__							:	Tuple   	=	False

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

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

       return status
def        lowercase_							(A : Tuple      ):
       assert isinstance(A		,					A      ) and (n > 2), "'N' must been an int and > 2"

       # beginList: contains all natural numbers from 2 up to N
       snake_case__							:	Optional[Any]   	=	list(range(2		,					n + 1      )      )

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

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

    # filters actual prime numbers.
       snake_case__							:	Union[str, Any]   	=	[x for x in begin_list if x != 0]

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

       return ans
def        lowercase_							(A : Optional[int]      ):
       assert isinstance(A		,					A      ) and (n > 2), "'N' must been an int and > 2"

       snake_case__							:	int   	=	[]

       # 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(A      ):
                     ans.append(A      )

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

       return ans
def        lowercase_							(A : str      ):
       assert isinstance(A		,					A      ) and number >= 0, "'number' must been an int and >= 0"

       snake_case__							:	Optional[int]   	=	[]  # this list will be returns of the function.

       # potential prime number factors.

       snake_case__							:	List[Any]   	=	2

       snake_case__							:	Dict   	=	number

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

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

       else:
              ans.append(A      )

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

       return ans
def        lowercase_							(A : Optional[int]      ):
       assert isinstance(A		,					A      ) and (
           number >= 0
       ), "'number' bust been an int and >= 0"

       snake_case__							:	Union[str, Any]   	=	0

       # prime factorization of 'number'
       snake_case__							:	Tuple   	=	prime_factorization(A      )

       snake_case__							:	Tuple   	=	max(A      )

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

       return ans
def        lowercase_							(A : List[Any]      ):
       assert isinstance(A		,					A      ) and (
           number >= 0
       ), "'number' bust been an int and >= 0"

       snake_case__							:	Tuple   	=	0

       # prime factorization of 'number'
       snake_case__							:	Union[str, Any]   	=	prime_factorization(A      )

       snake_case__							:	Union[str, Any]   	=	min(A      )

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

       return ans
def        lowercase_							(A : Union[str, Any]      ):
       assert isinstance(A		,					A      ), "'number' must been an int"
       assert isinstance(number % 2 == 0		,					A      ), "compare bust been from type bool"

       return number % 2 == 0
def        lowercase_							(A : Any      ):
       assert isinstance(A		,					A      ), "'number' must been an int"
       assert isinstance(number % 2 != 0		,					A      ), "compare bust been from type bool"

       return number % 2 != 0
def        lowercase_							(A : List[Any]      ):
       assert (
           isinstance(A		,					A      ) and (number > 2) and is_even(A      )
       ), "'number' must been an int, even and > 2"

       snake_case__							:	Dict   	=	[]  # this list will returned

       # creates a list of prime numbers between 2 up to 'number'
       snake_case__							:	Union[str, Any]   	=	get_prime_numbers(A      )
       snake_case__							:	Union[str, Any]   	=	len(A      )

       # run variable for while-loops.
       snake_case__							:	Dict   	=	0
       snake_case__							:	Union[str, Any]   	=	None

       # exit variable. for break up the loops
       snake_case__							:	str   	=	True

       while i < len_pn and loop:
              snake_case__							:	Union[str, Any]   	=	i + 1

              while j < len_pn and loop:
                     if prime_numbers[i] + prime_numbers[j] == number:
                            snake_case__							:	List[Any]   	=	False
                            ans.append(prime_numbers[i]      )
                            ans.append(prime_numbers[j]      )

                     j += 1

              i += 1

       # precondition
       assert (
           isinstance(A		,					A      )
           and (len(A      ) == 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        lowercase_							(A : Union[str, Any]		,					A : List[str]      ):
       assert (
           isinstance(A		,					A      )
           and isinstance(A		,					A      )
           and (numbera >= 0)
           and (numbera >= 0)
       ), "'number1' and 'number2' must been positive integer."

       snake_case__							:	Optional[Any]   	=	0

       while numbera != 0:
              snake_case__							:	List[Any]   	=	numbera % numbera
              snake_case__							:	List[Any]   	=	numbera
              snake_case__							:	Dict   	=	rest

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

       return numbera
def        lowercase_							(A : Optional[int]		,					A : Optional[int]      ):
       assert (
           isinstance(A		,					A      )
           and isinstance(A		,					A      )
           and (numbera >= 1)
           and (numbera >= 1)
       ), "'number1' and 'number2' must been positive integer."

       snake_case__							:	Optional[int]   	=	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'
              snake_case__							:	Tuple   	=	prime_factorization(A      )
              snake_case__							:	Dict   	=	prime_factorization(A      )

       elif numbera == 1 or numbera == 1:
              snake_case__							:	Optional[Any]   	=	[]
              snake_case__							:	List[str]   	=	[]
              snake_case__							:	Union[str, Any]   	=	max(A		,					A      )

       snake_case__							:	Tuple   	=	0
       snake_case__							:	Tuple   	=	0

       snake_case__							:	Optional[int]   	=	[]  # 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:
                            snake_case__							:	int   	=	prime_fac_a.count(A      )
                            snake_case__							:	Union[str, Any]   	=	prime_fac_a.count(A      )

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

                     else:
                            snake_case__							:	Union[str, Any]   	=	prime_fac_a.count(A      )

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

                     done.append(A      )

    # iterates through primeFac2
       for n in prime_fac_a:
              if n not in done:
                     snake_case__							:	int   	=	prime_fac_a.count(A      )

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

                     done.append(A      )

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

       return ans
def        lowercase_							(A : List[Any]      ):
       assert isinstance(A		,					A      ) and (n >= 0), "'number' must been a positive int"

       snake_case__							:	Union[str, Any]   	=	0
       snake_case__							:	Optional[int]   	=	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(A      ):
                     ans += 1

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

       return ans
def        lowercase_							(A : int		,					A : Union[str, Any]      ):
       assert (
           is_prime(A      ) and is_prime(A      ) and (p_number_a < p_number_a)
       ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

       snake_case__							:	str   	=	p_number_a + 1  # jump to the next number

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

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

       while number < p_number_a:
              ans.append(A      )

              number += 1

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

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

       # 'ans' contains not 'pNumber1' and 'pNumber2' !
       return ans
def        lowercase_							(A : int      ):
       assert isinstance(A		,					A      ) and (n >= 1), "'n' must been int and >= 1"

       snake_case__							:	Optional[int]   	=	[]  # will be returned.

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

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

       return ans
def        lowercase_							(A : str      ):
       assert isinstance(A		,					A      ) and (
           number > 1
       ), "'number' must been an int and >= 1"

       snake_case__							:	Optional[Any]   	=	get_divisors(A      )

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

       # summed all divisors up to 'number' (exclusive), hence [:-1]
       return sum(divisors[:-1]      ) == number
def        lowercase_							(A : Any		,					A : Optional[Any]      ):
       assert (
           isinstance(A		,					A      )
           and isinstance(A		,					A      )
           and (denominator != 0)
       ), "The arguments must been from type int and 'denominator' != 0"

       # build the greatest common divisor of numerator and denominator.
       snake_case__							:	Union[str, Any]   	=	gcd(abs(A      )		,					abs(A      )      )

       # precondition
       assert (
           isinstance(A		,					A      )
           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        lowercase_							(A : str      ):
       assert isinstance(A		,					A      ) and (n >= 0), "'n' must been a int and >= 0"

       snake_case__							:	List[Any]   	=	1  # this will be return.

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

       return ans





def        lowercase_							(A : int      ):
       assert isinstance(A		,					A      ) and (n >= 0), "'n' must been an int and >= 0"

       snake_case__							:	Any   	=	0
       snake_case__							:	Tuple   	=	1
       snake_case__							:	Dict   	=	1  # this will be return

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

       return ans











from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


a_   :Optional[Any]        =      {"configuration_reformer": ["REFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP", "ReformerConfig"]}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   :str        =      ["ReformerTokenizer"]

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   :int        =      ["ReformerTokenizerFast"]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   :List[str]        =      [
     "REFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "ReformerAttention",
     "ReformerForMaskedLM",
     "ReformerForQuestionAnswering",
     "ReformerForSequenceClassification",
     "ReformerLayer",
     "ReformerModel",
     "ReformerModelWithLMHead",
     "ReformerPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_reformer import REFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, ReformerConfig

 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_reformer import ReformerTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_reformer_fast import ReformerTokenizerFast

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_reformer import (
      REFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      ReformerAttention,
      ReformerForMaskedLM,
      ReformerForQuestionAnswering,
      ReformerForSequenceClassification,
      ReformerLayer,
      ReformerModel,
      ReformerModelWithLMHead,
      ReformerPreTrainedModel,
  )

else:
 import sys

 a_   :Optional[Any]        =      _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)






