



def 	_A	(   _UpperCamelCase      ,					_UpperCamelCase			):
				if a < b:
								return gcd(lowerCAmelCase_      ,					lowerCAmelCase_			)
				if a % b == 0:
								return b
				return gcd(lowerCAmelCase_      ,					a % b			)


def 	_A	(   _UpperCamelCase      ,					_UpperCamelCase      ,					_UpperCamelCase			):
				if y == 0:
								return 1
				_UpperCAmelCase						:  Optional[int]     					=	power(lowerCAmelCase_      ,					y // 2      ,					lowerCAmelCase_			) % mod
				_UpperCAmelCase						:  str     					=	(temp * temp) % mod
				if y % 2 == 1:
								_UpperCAmelCase						:  Tuple     					=	(temp * x) % mod
				return temp


def 	_A	(   _UpperCamelCase			):
				_UpperCAmelCase						:  List[Any]     					=	2
				while b < n:
								if gcd(lowerCAmelCase_      ,					lowerCAmelCase_			) == 1 and power(lowerCAmelCase_      ,					n - 1      ,					lowerCAmelCase_			) != 1:
												return False
								b += 1
				return True


if __name__ == "__main__":
					UpperCAmelCase__			:   Union[str, Any]      			=    int(input('Enter number: ').strip())
					if is_carmichael_number(number):
										print(F"""{number} is a Carmichael Number.""")
					else:
										print(F"""{number} is not a Carmichael Number.""")




import doctest

import projectq
from projectq.ops import H, Measure



def       lowerCAmelCase			(		lowerCAmelCase_			)->			int:
				lowerCAmelCase_			:   List[Any]     					=					quantum_engine.allocate_qubit()
				H | qubit
				Measure | qubit
				return int(lowerCAmelCase_			)


if __name__ == "__main__":
						doctest.testmod()

						# initialises a new quantum backend
						_UpperCAmelCase      :	str  =projectq.MainEngine()

						# Generate a list of 10 random numbers
						_UpperCAmelCase      :	Optional[int]  =[get_random_number(quantum_engine) for _ in range(10)]

						# Flushes the quantum engine from memory
						quantum_engine.flush()

						print("""Random numbers""", random_numbers_list)