




import math
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''

			if not isinstance(SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE   ):
						SCREAMING_SNAKE_CASE           =					f"""Input value of [number={number}] must be an integer"""
						raise TypeError(SCREAMING_SNAKE_CASE   )

			if number < 1:
						SCREAMING_SNAKE_CASE           =					f"""Input value of [number={number}] must be > 0"""
						raise ValueError(SCREAMING_SNAKE_CASE   )
			elif number == 1:
						return 3
			elif number == 2:
						return 5
			else:
						SCREAMING_SNAKE_CASE           =					int(math.log(number // 3					,	2   )   ) + 2

						SCREAMING_SNAKE_CASE           =					[3, 5]
						SCREAMING_SNAKE_CASE           =					2
						SCREAMING_SNAKE_CASE           =					3
						for block in range(1					,	SCREAMING_SNAKE_CASE   ):
									for _ in range(SCREAMING_SNAKE_CASE   ):
												proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]   )
												proth_index += 1
									increment *= 2

			return proth_list[number - 1]


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		for number in range(1_1):
				__A						:							Tuple							=  0
				try:
						__A						:							Optional[int]							=  proth(number)
				except ValueError:
						print(f'''ValueError: there is no {number}th Proth number''')
						continue

				print(f'''The {number}th Proth number: {value}''')









import os
import sys
import unittest


__A						:							Any							=  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
__A						:							List[Any]							=  os.path.join(git_repo_path, """src""", """diffusers""")




class 			UpperCAmelCase_      (   unittest.TestCase       ):




							'''simple docstring'''



							def    _UpperCAmelCase     (					self       :	Any			)			->					Optional[Any]:
										SCREAMING_SNAKE_CASE           =					find_backend("""    if not is_torch_available():"""			)
										self.assertEqual(a       ,     """torch"""			)

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

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

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





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

										# 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    _UpperCAmelCase     (					self       :	Any			)			->					int:
										SCREAMING_SNAKE_CASE           =					create_dummy_object("""CONSTANT"""       ,     """'torch'"""			)
										self.assertEqual(a       ,     """\nCONSTANT = None\n"""			)

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

										SCREAMING_SNAKE_CASE           =					"""
class FakeClass(metaclass=DummyObject):
    _backends = 'torch'

    def __init__(self, *args, **kwargs):
        requires_backends(self, 'torch')

    @classmethod
    def from_config(cls, *args, **kwargs):
        requires_backends(cls, 'torch')

    @classmethod
    def from_pretrained(cls, *args, **kwargs):
        requires_backends(cls, 'torch')
"""
										SCREAMING_SNAKE_CASE           =					create_dummy_object("""FakeClass"""       ,     """'torch'"""			)
										self.assertEqual(a       ,     a			)







							def    _UpperCAmelCase     (					self       :	Union[str, Any]			)			->					Union[str, Any]:
										SCREAMING_SNAKE_CASE           =					"""# This file is autogenerated by the command `make fix-copies`, do not edit.
from ..utils import DummyObject, requires_backends


CONSTANT = None


def function(*args, **kwargs):
    requires_backends(function, [\"torch\"])


class FakeClass(metaclass=DummyObject):
    _backends = [\"torch\"]

    def __init__(self, *args, **kwargs):
        requires_backends(self, [\"torch\"])

    @classmethod
    def from_config(cls, *args, **kwargs):
        requires_backends(cls, [\"torch\"])

    @classmethod
    def from_pretrained(cls, *args, **kwargs):
        requires_backends(cls, [\"torch\"])
"""
										SCREAMING_SNAKE_CASE           =					create_dummy_files({"""torch""": ["""CONSTANT""", """function""", """FakeClass"""]}			)
										self.assertEqual(dummy_files["""torch"""]       ,     a			)






