
def   lowerCAmelCase_						(					_snake_case      :  Dict = 10**12   )				->		int:







	'''simple docstring'''


	__magic_name__		:		List[str]	   =     1
	__magic_name__		:		Optional[Any]	   =     0

	__magic_name__		:		Any	   =     1
	__magic_name__		:		Optional[int]	   =     1

	while numerator <= 2 * min_total - 1:
		prev_numerator += 2 * numerator
		numerator += 2 * prev_numerator

		prev_denominator += 2 * denominator
		denominator += 2 * prev_denominator

	return (denominator + 1) // 2


if __name__ == "__main__":
				print(F"{solution() = }")




"""simple docstring"""







import os
import sys
import unittest


__lowercase    					=      os.path.abspath(os.path.dirname(os.path.dirname(os.path.dirname(__file__))))
sys.path.append(os.path.join(git_repo_path, """utils"""))

import check_dummies  # noqa: E402
from check_dummies import create_dummy_files, create_dummy_object, find_backend, read_init  # noqa: E402


# Align TRANSFORMERS_PATH in check_dummies with the current path
__lowercase    					=      os.path.join(git_repo_path, """src""", """diffusers""")






class 						_A  (  unittest.TestCase  ):







    """simple docstring"""




    def 	__snake_case							(					self				:    Any):
      a						:		List[Any]      							=			find_backend("    if not is_torch_available():")
      self.assertEqual(__UpperCAmelCase				, "torch")

      # backend_with_underscore = find_backend("    if not is_tensorflow_text_available():")
      # self.assertEqual(backend_with_underscore, "tensorflow_text")

      a						:		Dict      							=			find_backend("    if not (is_torch_available() and is_transformers_available()):")
      self.assertEqual(__UpperCAmelCase				, "torch_and_transformers")

      # double_backend_with_underscore = find_backend(
      #    "    if not (is_sentencepiece_available() and is_tensorflow_text_available()):"
      # )
      # self.assertEqual(double_backend_with_underscore, "sentencepiece_and_tensorflow_text")

      a						:		int      							=			find_backend(
          "    if not (is_torch_available() and is_transformers_available() and is_onnx_available()):")
      self.assertEqual(__UpperCAmelCase				, "torch_and_transformers_and_onnx")






    def 	__snake_case							(					self				:    Union[str, Any]):
      a						:		Dict      							=			read_init()
      # We don't assert on the exact list of keys to allow for smooth grow of backend-specific objects
      self.assertIn("torch"				, __UpperCAmelCase)
      self.assertIn("torch_and_transformers"				, __UpperCAmelCase)
      self.assertIn("flax_and_transformers"				, __UpperCAmelCase)
      self.assertIn("torch_and_transformers_and_onnx"				, __UpperCAmelCase)

      # Likewise, we can't assert on the exact content of a key
      self.assertIn("UNet2DModel"				, objects["torch"])
      self.assertIn("FlaxUNet2DConditionModel"				, objects["flax"])
      self.assertIn("StableDiffusionPipeline"				, objects["torch_and_transformers"])
      self.assertIn("FlaxStableDiffusionPipeline"				, objects["flax_and_transformers"])
      self.assertIn("LMSDiscreteScheduler"				, objects["torch_and_scipy"])
      self.assertIn("OnnxStableDiffusionPipeline"				, objects["torch_and_transformers_and_onnx"])






    def 	__snake_case							(					self				:    Tuple):
      a						:		Optional[int]      							=			create_dummy_object("CONSTANT"				, "'torch'")
      self.assertEqual(__UpperCAmelCase				, "\nCONSTANT = None\n")

      a						:		Dict      							=			create_dummy_object("function"				, "'torch'")
      self.assertEqual(
          __UpperCAmelCase				, "\ndef function(*args, **kwargs):\n    requires_backends(function, 'torch')\n")

      a						:		Optional[Any]      							=			"\nclass FakeClass(metaclass=DummyObject):\n    _backends = 'torch'\n\n    def __init__(self, *args, **kwargs):\n        requires_backends(self, 'torch')\n\n    @classmethod\n    def from_config(cls, *args, **kwargs):\n        requires_backends(cls, 'torch')\n\n    @classmethod\n    def from_pretrained(cls, *args, **kwargs):\n        requires_backends(cls, 'torch')\n"
      a						:		int      							=			create_dummy_object("FakeClass"				, "'torch'")
      self.assertEqual(__UpperCAmelCase				, __UpperCAmelCase)






    def 	__snake_case							(					self				:    List[str]):
      a						:		List[str]      							=			"# This file is autogenerated by the command `make fix-copies`, do not edit.\nfrom ..utils import DummyObject, requires_backends\n\n\nCONSTANT = None\n\n\ndef function(*args, **kwargs):\n    requires_backends(function, [\"torch\"])\n\n\nclass FakeClass(metaclass=DummyObject):\n    _backends = [\"torch\"]\n\n    def __init__(self, *args, **kwargs):\n        requires_backends(self, [\"torch\"])\n\n    @classmethod\n    def from_config(cls, *args, **kwargs):\n        requires_backends(cls, [\"torch\"])\n\n    @classmethod\n    def from_pretrained(cls, *args, **kwargs):\n        requires_backends(cls, [\"torch\"])\n"
      a						:		Tuple      							=			create_dummy_files({"torch": ["CONSTANT", "function", "FakeClass"]})
      self.assertEqual(dummy_files["torch"]				, __UpperCAmelCase)






