


'''simple docstring'''







from math import sqrt






def 			lowercase				(_A					):







       """simple docstring"""







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

       _lowerCAmelCase    :							List[str]   			=       True

       # 0 and 1 are none primes.
       if number <= 1:
              _lowerCAmelCase    :							List[Any]   			=       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:
                     _lowerCAmelCase    :							Optional[Any]   			=       False
                     break

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

       return status






def 			lowercase				(_A					):







       """simple docstring"""







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

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

       _lowerCAmelCase    :							Tuple   			=       []  # 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):
                            _lowerCAmelCase    :							Dict   			=       0

    # filters actual prime numbers.
       _lowerCAmelCase    :							Optional[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					):







       """simple docstring"""







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

       _lowerCAmelCase    :							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					):







       """simple docstring"""







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

       _lowerCAmelCase    :							Union[str, Any]   			=       []  # this list will be returns of the function.

       # potential prime number factors.

       _lowerCAmelCase    :							List[Any]   			=       2

       _lowerCAmelCase    :							List[str]   			=       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					):







       """simple docstring"""







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

       _lowerCAmelCase    :							Any   			=       0

       # prime factorization of 'number'
       _lowerCAmelCase    :							Optional[int]   			=       prime_factorization(_A					)

       _lowerCAmelCase    :							List[str]   			=       max(_A					)

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

       return ans






def 			lowercase				(_A					):







       """simple docstring"""







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

       _lowerCAmelCase    :							List[Any]   			=       0

       # prime factorization of 'number'
       _lowerCAmelCase    :							List[Any]   			=       prime_factorization(_A					)

       _lowerCAmelCase    :							int   			=       min(_A					)

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

       return ans






def 			lowercase				(_A					):







       """simple docstring"""







       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					):







       """simple docstring"""







       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					):







       """simple docstring"""







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

       _lowerCAmelCase    :							str   			=       []  # this list will returned

       # creates a list of prime numbers between 2 up to 'number'
       _lowerCAmelCase    :							int   			=       get_prime_numbers(_A					)
       _lowerCAmelCase    :							List[str]   			=       len(_A					)

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

       # exit variable. for break up the loops
       _lowerCAmelCase    :							Union[str, Any]   			=       True

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

              while j < len_pn and loop:
                     if prime_numbers[i] + prime_numbers[j] == number:
                            _lowerCAmelCase    :							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   ,						_A					):







       """simple docstring"""







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

       _lowerCAmelCase    :							str   			=       0

       while numbera != 0:
              _lowerCAmelCase    :							List[Any]   			=       numbera % numbera
              _lowerCAmelCase    :							Any   			=       numbera
              _lowerCAmelCase    :							Union[str, Any]   			=       rest

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

       return numbera






def 			lowercase				(_A   ,						_A					):







       """simple docstring"""







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

       _lowerCAmelCase    :							List[Any]   			=       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'
              _lowerCAmelCase    :							Optional[int]   			=       prime_factorization(_A					)
              _lowerCAmelCase    :							int   			=       prime_factorization(_A					)

       elif numbera == 1 or numbera == 1:
              _lowerCAmelCase    :							Any   			=       []
              _lowerCAmelCase    :							List[str]   			=       []
              _lowerCAmelCase    :							int   			=       max(_A   ,						_A					)

       _lowerCAmelCase    :							int   			=       0
       _lowerCAmelCase    :							int   			=       0

       _lowerCAmelCase    :							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:
                            _lowerCAmelCase    :							Tuple   			=       prime_fac_a.count(_A					)
                            _lowerCAmelCase    :							Optional[Any]   			=       prime_fac_a.count(_A					)

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

                     else:
                            _lowerCAmelCase    :							Optional[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:
                     _lowerCAmelCase    :							Any   			=       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					):







       """simple docstring"""







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

       _lowerCAmelCase    :							Optional[int]   			=       0
       _lowerCAmelCase    :							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(_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   ,						_A					):







       """simple docstring"""







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

       _lowerCAmelCase    :							Union[str, Any]   			=       p_number_a + 1  # jump to the next number

       _lowerCAmelCase    :							Optional[int]   			=       []  # 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					):







       """simple docstring"""







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

       _lowerCAmelCase    :							List[str]   			=       []  # 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					):







       """simple docstring"""







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

       _lowerCAmelCase    :							Union[str, 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   ,						_A					):







       """simple docstring"""







       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.
       _lowerCAmelCase    :							Optional[int]   			=       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					):







       """simple docstring"""







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

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

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

       return ans






def 			lowercase				(_A					):







       """simple docstring"""







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

       _lowerCAmelCase    :							int   			=       0
       _lowerCAmelCase    :							Optional[int]   			=       1
       _lowerCAmelCase    :							str   			=       1  # this will be return

       for _ in range(n - 1					):
              _lowerCAmelCase    :							Union[str, Any]   			=       ans
              ans += fiba
              _lowerCAmelCase    :							Any   			=       tmp

       return ans





'''simple docstring'''







from typing import TYPE_CHECKING

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


lowerCAmelCase    :     Optional[int]					=						{
    """configuration_mctct""": ["""MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """MCTCTConfig"""],
    """feature_extraction_mctct""": ["""MCTCTFeatureExtractor"""],
    """processing_mctct""": ["""MCTCTProcessor"""],
}


try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowerCAmelCase    :     List[str]					=						[
           """MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST""",
           """MCTCTForCTC""",
           """MCTCTModel""",
           """MCTCTPreTrainedModel""",
       ]


if TYPE_CHECKING:
       from .configuration_mctct import MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP, MCTCTConfig
       from .feature_extraction_mctct import MCTCTFeatureExtractor
       from .processing_mctct import MCTCTProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_mctct import MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST, MCTCTForCTC, MCTCTModel, MCTCTPreTrainedModel

else:
       import sys

       lowerCAmelCase    :     Tuple					=						_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

