



'''simple docstring'''





from math import sqrt




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  True

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

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

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

     return status




def lowerCAmelCase  (__A):



     """simple docstring"""



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

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

     _a      =  []  # this list will be returns.

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

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

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  []

     # 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(lowercase__):
               ans.append(lowercase__)

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

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

     # potential prime number factors.

     _a      =  2

     _a      =  number

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

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

     else:
          ans.append(lowercase__)

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  0

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

     _a      =  max(lowercase__)

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  0

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

     _a      =  min(lowercase__)

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     return number % 2 == 0




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     return number % 2 != 0




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  []  # this list will returned

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

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

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

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

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

               j += 1

          i += 1

     # precondition
     assert (
         isinstance(lowercase__  ,	lowercase__)
         and (len(lowercase__) == 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):



     """simple docstring"""



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

     _a      =  0

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

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

     return numbera




def lowerCAmelCase  (__A  ,	__A):



     """simple docstring"""



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

     _a      =  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      =  prime_factorization(lowercase__)
          _a      =  prime_factorization(lowercase__)

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

     _a      =  0
     _a      =  0

     _a      =  []  # 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      =  prime_fac_a.count(lowercase__)
                    _a      =  prime_fac_a.count(lowercase__)

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

               else:
                    _a      =  prime_fac_a.count(lowercase__)

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

               done.append(lowercase__)

    # iterates through primeFac2
     for n in prime_fac_a:
          if n not in done:
               _a      =  prime_fac_a.count(lowercase__)

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

               done.append(lowercase__)

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  0
     _a      =  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(lowercase__):
               ans += 1

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

     return ans




def lowerCAmelCase  (__A  ,	__A):



     """simple docstring"""



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

     _a      =  p_number_a + 1  # jump to the next number

     _a      =  []  # this list will be returns.

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

     while number < p_number_a:
          ans.append(lowercase__)

          number += 1

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

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

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




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  []  # will be returned.

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

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

     _a      =  get_divisors(lowercase__)

     # precondition
     assert (
         isinstance(lowercase__  ,	lowercase__)
         and (divisors[0] == 1)
         and (divisors[len(lowercase__) - 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):



     """simple docstring"""



     assert (
         isinstance(lowercase__  ,	lowercase__)
         and isinstance(lowercase__  ,	lowercase__)
         and (denominator != 0)
     ), "The arguments must been from type int and 'denominator' != 0"

     # build the greatest common divisor of numerator and denominator.
     _a      =  gcd(abs(lowercase__)  ,	abs(lowercase__))

     # precondition
     assert (
         isinstance(lowercase__  ,	lowercase__)
         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):



     """simple docstring"""



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

     _a      =  1  # this will be return.

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

     return ans




def lowerCAmelCase  (__A):



     """simple docstring"""



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

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

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

     return ans







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCAmelCase	: Any  				={'configuration_vit_msn': ['VIT_MSN_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ViTMSNConfig']}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__lowerCAmelCase	: int  				=[
						    'VIT_MSN_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'ViTMSNModel',
						    'ViTMSNForImageClassification',
						    'ViTMSNPreTrainedModel',
						]

if TYPE_CHECKING:
						from .configuration_vit_msn import VIT_MSN_PRETRAINED_CONFIG_ARCHIVE_MAP, ViTMSNConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_vit_msn import (
												    VIT_MSN_PRETRAINED_MODEL_ARCHIVE_LIST,
												    ViTMSNForImageClassification,
												    ViTMSNModel,
												    ViTMSNPreTrainedModel,
												)

else:
						import sys

						__lowerCAmelCase	: Union[str, Any]  				=_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
