


import inspect
import unittest






class       _UpperCamelCase    (					unittest.TestCase				):

				"""simple docstring"""







				def      _UpperCAmelCase					(						self   )	->				Any:
					try:
						import diffusers  # noqa: F401
					except ImportError:
						assert False

				def      _UpperCAmelCase					(						self   )	->				List[str]:
					import diffusers
					from diffusers.dependency_versions_table import deps

					A								=				inspect.getmembers(a__				,   inspect.isclass   )

					for cls_name, cls_module in all_classes:
						if "dummy_" in cls_module.__module__:
							for backend in cls_module._backends:
								if backend == "k_diffusion":
									A								=				"""k-diffusion"""
								elif backend == "invisible_watermark":
									A								=				"""invisible-watermark"""
								assert backend in deps, f'{backend} is not in the deps table!'







import math





def   _lowerCAmelCase				(   UpperCamelCase__:     int						) ->   bool:





	"""simple docstring"""







	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5							,					int(math.sqrt(UpperCamelCase__						) + 1						)							,					6						):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True





def   _lowerCAmelCase				(   UpperCamelCase__:     float = 0.1						) ->   int:





	"""simple docstring"""







	A								=				3
	A								=				3

	while primes / (2 * j - 1) >= ratio:
		for i in range(j * j + j + 1							,					(j + 2) * (j + 2)							,					j + 1						):
			primes += is_prime(UpperCamelCase__						)
		j += 2
	return j


if __name__ == "__main__":
				import doctest

				doctest.testmod()



