





from math import sqrt






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

   a__	:						str      		=  True

   # 0 and 1 are none primes.
   if number <= 1:
      a__	:						Any      		=  False

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

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

   return status






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

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

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

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

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

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

   return ans






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

   a__	:						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(lowerCamelCase   ):
         ans.append(lowerCamelCase   )

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

   return ans






def       _A  (      lowerCamelCase   ):
   assert isinstance(lowerCamelCase							, lowerCamelCase   ) and number >= 0, "'number' must been an int and >= 0"

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

   # potential prime number factors.

   a__	:						List[str]      		=  2

   a__	:						int      		=  number

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

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

   else:
      ans.append(lowerCamelCase   )

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

   return ans






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

   a__	:						List[Any]      		=  0

   # prime factorization of 'number'
   a__	:						List[Any]      		=  prime_factorization(lowerCamelCase   )

   a__	:						str      		=  max(lowerCamelCase   )

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

   return ans






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

   a__	:						Optional[Any]      		=  0

   # prime factorization of 'number'
   a__	:						Optional[Any]      		=  prime_factorization(lowerCamelCase   )

   a__	:						List[Any]      		=  min(lowerCamelCase   )

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

   return ans






def       _A  (      lowerCamelCase   ):
   assert isinstance(lowerCamelCase							, lowerCamelCase   ), "'number' must been an int"
   assert isinstance(number % 2 == 0							, lowerCamelCase   ), "compare bust been from type bool"

   return number % 2 == 0






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

   return number % 2 != 0






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

   a__	:						Optional[Any]      		=  []  # this list will returned

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

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

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

   while i < len_pn and loop:
      a__	:						List[str]      		=  i + 1

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

         j += 1

      i += 1

   # precondition
   assert (
       isinstance(lowerCamelCase							, lowerCamelCase   )
       and (len(lowerCamelCase   ) == 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       _A  (      lowerCamelCase							, lowerCamelCase   ):
   assert (
       isinstance(lowerCamelCase							, lowerCamelCase   )
       and isinstance(lowerCamelCase							, lowerCamelCase   )
       and (numbera >= 0)
       and (numbera >= 0)
   ), "'number1' and 'number2' must been positive integer."

   a__	:						Union[str, Any]      		=  0

   while numbera != 0:
      a__	:						Tuple      		=  numbera % numbera
      a__	:						str      		=  numbera
      a__	:						Union[str, Any]      		=  rest

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

   return numbera






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

   a__	:						Tuple      		=  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'
      a__	:						Optional[Any]      		=  prime_factorization(lowerCamelCase   )
      a__	:						List[Any]      		=  prime_factorization(lowerCamelCase   )

   elif numbera == 1 or numbera == 1:
      a__	:						Optional[int]      		=  []
      a__	:						Optional[int]      		=  []
      a__	:						Dict      		=  max(lowerCamelCase							, lowerCamelCase   )

   a__	:						Any      		=  0
   a__	:						Optional[int]      		=  0

   a__	:						List[Any]      		=  []  # 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:
            a__	:						str      		=  prime_fac_a.count(lowerCamelCase   )
            a__	:						List[Any]      		=  prime_fac_a.count(lowerCamelCase   )

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

         else:
            a__	:						Union[str, Any]      		=  prime_fac_a.count(lowerCamelCase   )

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

         done.append(lowerCamelCase   )

    # iterates through primeFac2
   for n in prime_fac_a:
      if n not in done:
         a__	:						Dict      		=  prime_fac_a.count(lowerCamelCase   )

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

         done.append(lowerCamelCase   )

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

   return ans






def       _A  (      lowerCamelCase   ):
   assert isinstance(lowerCamelCase							, lowerCamelCase   ) and (n >= 0), "'number' must been a positive int"

   a__	:						str      		=  0
   a__	:						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(lowerCamelCase   ):
         ans += 1

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

   return ans






def       _A  (      lowerCamelCase							, lowerCamelCase   ):
   assert (
       is_prime(lowerCamelCase   ) and is_prime(lowerCamelCase   ) and (p_number_a < p_number_a)
   ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

   a__	:						int      		=  p_number_a + 1  # jump to the next number

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

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

   while number < p_number_a:
      ans.append(lowerCamelCase   )

      number += 1

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

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

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






def       _A  (      lowerCamelCase   ):
   assert isinstance(lowerCamelCase							, lowerCamelCase   ) and (n >= 1), "'n' must been int and >= 1"

   a__	:						Any      		=  []  # will be returned.

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

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

   return ans






def       _A  (      lowerCamelCase   ):
   assert isinstance(lowerCamelCase							, lowerCamelCase   ) and (
       number > 1
   ), "'number' must been an int and >= 1"

   a__	:						int      		=  get_divisors(lowerCamelCase   )

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

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






def       _A  (      lowerCamelCase							, lowerCamelCase   ):
   assert (
       isinstance(lowerCamelCase							, lowerCamelCase   )
       and isinstance(lowerCamelCase							, lowerCamelCase   )
       and (denominator != 0)
   ), "The arguments must been from type int and 'denominator' != 0"

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

   # precondition
   assert (
       isinstance(lowerCamelCase							, lowerCamelCase   )
       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       _A  (      lowerCamelCase   ):
   assert isinstance(lowerCamelCase							, lowerCamelCase   ) and (n >= 0), "'n' must been a int and >= 0"

   a__	:						Dict      		=  1  # this will be return.

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

   return ans






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

   a__	:						Tuple      		=  0
   a__	:						int      		=  1
   a__	:						List[str]      		=  1  # this will be return

   for _ in range(n - 1   ):
      a__	:						List[Any]      		=  ans
      ans += fiba
      a__	:						Any      		=  tmp

   return ans








from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


SCREAMING_SNAKE_CASE__       :			Any			      =						{"""configuration_sew""": ["""SEW_PRETRAINED_CONFIG_ARCHIVE_MAP""", """SEWConfig"""]}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  SCREAMING_SNAKE_CASE__       :			Union[str, Any]			      =						[
      """SEW_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """SEWForCTC""",
      """SEWForSequenceClassification""",
      """SEWModel""",
      """SEWPreTrainedModel""",
  ]

if TYPE_CHECKING:
  from .configuration_sew import SEW_PRETRAINED_CONFIG_ARCHIVE_MAP, SEWConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_sew import (
        SEW_PRETRAINED_MODEL_ARCHIVE_LIST,
        SEWForCTC,
        SEWForSequenceClassification,
        SEWModel,
        SEWPreTrainedModel,
    )


else:
  import sys

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

