
"""simple docstring"""
def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__      ):


	"""simple docstring"""






	if a < b:
		return gcd(UpperCamelCase__				,     UpperCamelCase__      )
	if a % b == 0:
		return b
	return gcd(UpperCamelCase__				,     a % b      )




def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__      ):


	"""simple docstring"""






	if y == 0:
		return 1
	_UpperCAmelCase =						power(UpperCamelCase__				,     y // 2				,     UpperCamelCase__      ) % mod
	_UpperCAmelCase =						(temp * temp) % mod
	if y % 2 == 1:
		_UpperCAmelCase =						(temp * x) % mod
	return temp




def     __lowerCamelCase  (		UpperCamelCase__      ):


	"""simple docstring"""






	_UpperCAmelCase =						2
	while b < n:
		if gcd(UpperCamelCase__				,     UpperCamelCase__      ) == 1 and power(UpperCamelCase__				,     n - 1				,     UpperCamelCase__      ) != 1:
			return False
		b += 1
	return True


if __name__ == "__main__":
			__magic_name__		       =				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.''')






"""simple docstring"""
def     __lowerCamelCase  (		UpperCamelCase__      ):


	"""simple docstring"""






	if not isinstance(UpperCamelCase__				,     UpperCamelCase__      ):
		raise TypeError("recursive_lucas_number accepts only integer arguments."      )
	if n_th_number == 0:
		return 2
	if n_th_number == 1:
		return 1

	return recursive_lucas_number(n_th_number - 1      ) + recursive_lucas_number(
	    n_th_number - 2      )




def     __lowerCamelCase  (		UpperCamelCase__      ):


	"""simple docstring"""






	if not isinstance(UpperCamelCase__				,     UpperCamelCase__      ):
		raise TypeError("dynamic_lucas_number accepts only integer arguments."      )
	_UpperCAmelCase ,      _UpperCAmelCase =						2, 1
	for _ in range(UpperCamelCase__      ):
		_UpperCAmelCase ,      _UpperCAmelCase =						b, a + b
	return a


if __name__ == "__main__":
			from doctest import testmod

			testmod()
			__magic_name__		       =				int(input('''Enter the number of terms in lucas series:\n''').strip())
			print('''Using recursive function to calculate lucas series:''')
			print(''' '''.join(str(recursive_lucas_number(i)) for i in range(n)))
			print('''\nUsing dynamic function to calculate lucas series:''')
			print(''' '''.join(str(dynamic_lucas_number(i)) for i in range(n)))




