
'''simple docstring'''






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


UpperCAmelCase_							: Optional[Any] =							{
    'configuration_transfo_xl': ['TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP', 'TransfoXLConfig'],
    'tokenization_transfo_xl': ['TransfoXLCorpus', 'TransfoXLTokenizer'],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 UpperCAmelCase_							: int =							[
     'TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST',
     'AdaptiveEmbedding',
     'TransfoXLForSequenceClassification',
     'TransfoXLLMHeadModel',
     'TransfoXLModel',
     'TransfoXLPreTrainedModel',
     'load_tf_weights_in_transfo_xl',
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 UpperCAmelCase_							: Tuple =							[
     'TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST',
     'TFAdaptiveEmbedding',
     'TFTransfoXLForSequenceClassification',
     'TFTransfoXLLMHeadModel',
     'TFTransfoXLMainLayer',
     'TFTransfoXLModel',
     'TFTransfoXLPreTrainedModel',
 ]


if TYPE_CHECKING:
 from .configuration_transfo_xl import TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP, TransfoXLConfig
 from .tokenization_transfo_xl import TransfoXLCorpus, TransfoXLTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_transfo_xl import (
      TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
      AdaptiveEmbedding,
      TransfoXLForSequenceClassification,
      TransfoXLLMHeadModel,
      TransfoXLModel,
      TransfoXLPreTrainedModel,
      load_tf_weights_in_transfo_xl,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_transfo_xl import (
      TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFAdaptiveEmbedding,
      TFTransfoXLForSequenceClassification,
      TFTransfoXLLMHeadModel,
      TFTransfoXLMainLayer,
      TFTransfoXLModel,
      TFTransfoXLPreTrainedModel,
  )

else:
 import sys

 UpperCAmelCase_							: Tuple =							_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




from math import sqrt

def 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (
          number >= 0
      ), "'number' must been an int and positive"

      lowercase__  =	True

      # 0 and 1 are none primes.
      if number <= 1:
            lowercase__  =	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:
                  lowercase__  =	False
                  break

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

      return status

def 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (n > 2), "'N' must been an int and > 2"

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

      lowercase__  =	[]  # 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):
                        lowercase__  =	0

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

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

      return ans

def 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (n > 2), "'N' must been an int and > 2"

      lowercase__  =	[]

      # 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 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and number >= 0, "'number' must been an int and >= 0"

      lowercase__  =	[]  # this list will be returns of the function.

      # potential prime number factors.

      lowercase__  =	2

      lowercase__  =	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 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (
          number >= 0
      ), "'number' bust been an int and >= 0"

      lowercase__  =	0

      # prime factorization of 'number'
      lowercase__  =	prime_factorization(A__						)

      lowercase__  =	max(A__						)

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

      return ans

def 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (
          number >= 0
      ), "'number' bust been an int and >= 0"

      lowercase__  =	0

      # prime factorization of 'number'
      lowercase__  =	prime_factorization(A__						)

      lowercase__  =	min(A__						)

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

      return ans

def 	_lowerCAmelCase (    A__						):
      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 	_lowerCAmelCase (    A__						):
      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 	_lowerCAmelCase (    A__						):
      assert (
          isinstance(A__    ,	A__						) and (number > 2) and is_even(A__						)
      ), "'number' must been an int, even and > 2"

      lowercase__  =	[]  # this list will returned

      # creates a list of prime numbers between 2 up to 'number'
      lowercase__  =	get_prime_numbers(A__						)
      lowercase__  =	len(A__						)

      # run variable for while-loops.
      lowercase__  =	0
      lowercase__  =	None

      # exit variable. for break up the loops
      lowercase__  =	True

      while i < len_pn and loop:
            lowercase__  =	i + 1

            while j < len_pn and loop:
                  if prime_numbers[i] + prime_numbers[j] == number:
                        lowercase__  =	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 	_lowerCAmelCase (    A__    ,	A__						):
      assert (
          isinstance(A__    ,	A__						)
          and isinstance(A__    ,	A__						)
          and (numbera >= 0)
          and (numbera >= 0)
      ), "'number1' and 'number2' must been positive integer."

      lowercase__  =	0

      while numbera != 0:
            lowercase__  =	numbera % numbera
            lowercase__  =	numbera
            lowercase__  =	rest

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

      return numbera

def 	_lowerCAmelCase (    A__    ,	A__						):
      assert (
          isinstance(A__    ,	A__						)
          and isinstance(A__    ,	A__						)
          and (numbera >= 1)
          and (numbera >= 1)
      ), "'number1' and 'number2' must been positive integer."

      lowercase__  =	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__  =	prime_factorization(A__						)
            lowercase__  =	prime_factorization(A__						)

      elif numbera == 1 or numbera == 1:
            lowercase__  =	[]
            lowercase__  =	[]
            lowercase__  =	max(A__    ,	A__						)

      lowercase__  =	0
      lowercase__  =	0

      lowercase__  =	[]  # 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__  =	prime_fac_a.count(A__						)
                        lowercase__  =	prime_fac_a.count(A__						)

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

                  else:
                        lowercase__  =	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:
                  lowercase__  =	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 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (n >= 0), "'number' must been a positive int"

      lowercase__  =	0
      lowercase__  =	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 	_lowerCAmelCase (    A__    ,	A__						):
      assert (
          is_prime(A__						) and is_prime(A__						) and (p_number_a < p_number_a)
      ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

      lowercase__  =	p_number_a + 1  # jump to the next number

      lowercase__  =	[]  # 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 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (n >= 1), "'n' must been int and >= 1"

      lowercase__  =	[]  # 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 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (
          number > 1
      ), "'number' must been an int and >= 1"

      lowercase__  =	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 	_lowerCAmelCase (    A__    ,	A__						):
      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.
      lowercase__  =	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 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						) and (n >= 0), "'n' must been a int and >= 0"

      lowercase__  =	1  # this will be return.

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

      return ans

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

      lowercase__  =	0
      lowercase__  =	1
      lowercase__  =	1  # this will be return

      for _ in range(n - 1						):
            lowercase__  =	ans
            ans += fiba
            lowercase__  =	tmp

      return ans
