




from math import sqrt







def 			lowerCamelCase_		(       UpperCamelCase__				:      int      )     ->       bool:





				"""simple docstring"""


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

				__lowerCamelCase		       =    True

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

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

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

				return status







def 			lowerCamelCase_		(       UpperCamelCase__				:      str      )     ->       Tuple:





				"""simple docstring"""


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

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

				__lowerCamelCase		       =    []  # this list will be returns.

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

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

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      List[Any]      )     ->       List[str]:





				"""simple docstring"""


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

				__lowerCamelCase		       =    []

				# 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(UpperCamelCase__      ):
												ans.append(UpperCamelCase__      )

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      Optional[int]      )     ->       int:





				"""simple docstring"""


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

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

				# potential prime number factors.

				__lowerCamelCase		       =    2

				__lowerCamelCase		       =    number

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

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

				else:
								ans.append(UpperCamelCase__      )

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      Tuple      )     ->       Optional[int]:





				"""simple docstring"""


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

				__lowerCamelCase		       =    0

				# prime factorization of 'number'
				__lowerCamelCase		       =    prime_factorization(UpperCamelCase__      )

				__lowerCamelCase		       =    max(UpperCamelCase__      )

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      Union[str, Any]      )     ->       Tuple:





				"""simple docstring"""


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

				__lowerCamelCase		       =    0

				# prime factorization of 'number'
				__lowerCamelCase		       =    prime_factorization(UpperCamelCase__      )

				__lowerCamelCase		       =    min(UpperCamelCase__      )

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      Optional[int]      )     ->       Optional[int]:





				"""simple docstring"""


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

				return number % 2 == 0







def 			lowerCamelCase_		(       UpperCamelCase__				:      str      )     ->       str:





				"""simple docstring"""


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

				return number % 2 != 0







def 			lowerCamelCase_		(       UpperCamelCase__				:      Union[str, Any]      )     ->       Optional[Any]:





				"""simple docstring"""


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

				__lowerCamelCase		       =    []  # this list will returned

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

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

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

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

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

												j += 1

								i += 1

				# precondition
				assert (
				    isinstance(UpperCamelCase__ ,     UpperCamelCase__      )
				    and (len(UpperCamelCase__      ) == 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_		(       UpperCamelCase__				:      Any ,     UpperCamelCase__				:      Optional[int]      )     ->       Optional[Any]:





				"""simple docstring"""


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

				__lowerCamelCase		       =    0

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

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

				return numbera







def 			lowerCamelCase_		(       UpperCamelCase__				:      Dict ,     UpperCamelCase__				:      str      )     ->       int:





				"""simple docstring"""


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

				__lowerCamelCase		       =    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		       =    prime_factorization(UpperCamelCase__      )
								__lowerCamelCase		       =    prime_factorization(UpperCamelCase__      )

				elif numbera == 1 or numbera == 1:
								__lowerCamelCase		       =    []
								__lowerCamelCase		       =    []
								__lowerCamelCase		       =    max(UpperCamelCase__ ,     UpperCamelCase__      )

				__lowerCamelCase		       =    0
				__lowerCamelCase		       =    0

				__lowerCamelCase		       =    []  # 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		       =    prime_fac_a.count(UpperCamelCase__      )
																__lowerCamelCase		       =    prime_fac_a.count(UpperCamelCase__      )

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

												else:
																__lowerCamelCase		       =    prime_fac_a.count(UpperCamelCase__      )

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

												done.append(UpperCamelCase__      )

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

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

												done.append(UpperCamelCase__      )

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      Dict      )     ->       str:





				"""simple docstring"""


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

				__lowerCamelCase		       =    0
				__lowerCamelCase		       =    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(UpperCamelCase__      ):
												ans += 1

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      str ,     UpperCamelCase__				:      Tuple      )     ->       Tuple:





				"""simple docstring"""


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

				__lowerCamelCase		       =    p_number_a + 1  # jump to the next number

				__lowerCamelCase		       =    []  # this list will be returns.

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

				while number < p_number_a:
								ans.append(UpperCamelCase__      )

								number += 1

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

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

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







def 			lowerCamelCase_		(       UpperCamelCase__				:      int      )     ->       Optional[Any]:





				"""simple docstring"""


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

				__lowerCamelCase		       =    []  # will be returned.

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

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      Dict      )     ->       Optional[int]:





				"""simple docstring"""


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

				__lowerCamelCase		       =    get_divisors(UpperCamelCase__      )

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

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







def 			lowerCamelCase_		(       UpperCamelCase__				:      Optional[int] ,     UpperCamelCase__				:      List[str]      )     ->       List[Any]:





				"""simple docstring"""


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

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

				# precondition
				assert (
				    isinstance(UpperCamelCase__ ,     UpperCamelCase__      )
				    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_		(       UpperCamelCase__				:      List[str]      )     ->       Optional[Any]:





				"""simple docstring"""


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

				__lowerCamelCase		       =    1  # this will be return.

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

				return ans







def 			lowerCamelCase_		(       UpperCamelCase__				:      Union[str, Any]      )     ->       Union[str, Any]:





				"""simple docstring"""


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

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

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

				return ans








from ..utils import DummyObject, requires_backends







class     __lowerCAmelCase (       metaclass=__magic_name__ ):

			"""simple docstring"""







			snake_case_   		=       ['''onnx''']


			def __init__(      self			,						*lowerCamelCase__			,						**lowerCamelCase__							)    ->      Optional[Any]:



							'''simple docstring'''
							requires_backends(self			,						['onnx']							)


			@classmethod
			def       lowercase_    (      cls			,						*lowerCamelCase__			,						**lowerCamelCase__							)    ->      Dict:



							'''simple docstring'''
							requires_backends(cls			,						['onnx']							)






			@classmethod
			def       lowercase_    (      cls			,						*lowerCamelCase__			,						**lowerCamelCase__							)    ->      List[str]:



							'''simple docstring'''
							requires_backends(cls			,						['onnx']							)


