


def 				lowerCamelCase__	(      a	:   Any = 10**12				)    ->	int:





			"""simple docstring"""
			a__ :List[Any]						  =    1
			a__ :Optional[int]						  =    0

			a__ :str						  =    1
			a__ :List[str]						  =    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() = }''')






# Copyright 2021 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import argparse

from ...utils.dataclasses import (
    ComputeEnvironment,
    DistributedType,
    DynamoBackend,
    PrecisionType,
    SageMakerDistributedType,
)
from ..menu import BulletMenu


snake_case__			 =						[
    '''EAGER''',
    '''AOT_EAGER''',
    '''INDUCTOR''',
    '''NVFUSER''',
    '''AOT_NVFUSER''',
    '''AOT_CUDAGRAPHS''',
    '''OFI''',
    '''FX2TRT''',
    '''ONNXRT''',
    '''IPEX''',
]


def 				lowerCamelCase__	(      a	:   Optional[Any]	,  a	:   Tuple=None	,  a	:   int=None	,  a	:   List[str]=None				)    ->	int:





			"""simple docstring"""
			a__ :Tuple						  =    True
			while ask_again:
						a__ :str						  =    input(a				)
						try:
									if default is not None and len(a				) == 0:
												return default
									return convert_value(a				) if convert_value is not None else result
						except Exception:
									if error_message is not None:
												print(a				)


def 				lowerCamelCase__	(      a	:   int	,  a	:   Union[str, Any]=[]	,  a	:   str=None	,  a	:   str=0				)    ->	List[str]:





			"""simple docstring"""
			a__ :str						  =    BulletMenu(a	,  a				)
			a__ :int						  =    menu.run(default_choice=a				)
			return convert_value(a				) if convert_value is not None else result


def 				lowerCamelCase__	(      a	:   Optional[Any]				)    ->	Dict:





			"""simple docstring"""
			a__ :str						  =    int(a				)
			return ComputeEnvironment(["LOCAL_MACHINE", "AMAZON_SAGEMAKER"][value]				)


def 				lowerCamelCase__	(      a	:   Tuple				)    ->	List[str]:





			"""simple docstring"""
			a__ :Union[str, Any]						  =    int(a				)
			return DistributedType(["NO", "MULTI_CPU", "MULTI_XPU", "MULTI_GPU", "MULTI_NPU", "TPU"][value]				)


def 				lowerCamelCase__	(      a	:   List[Any]				)    ->	str:





			"""simple docstring"""
			a__ :int						  =    int(a				)
			return DynamoBackend(DYNAMO_BACKENDS[value]				).value


def 				lowerCamelCase__	(      a	:   Any				)    ->	Union[str, Any]:





			"""simple docstring"""
			a__ :Optional[Any]						  =    int(a				)
			return PrecisionType(["no", "fp16", "bf16", "fp8"][value]				)


def 				lowerCamelCase__	(      a	:   List[Any]				)    ->	Union[str, Any]:





			"""simple docstring"""
			a__ :Optional[Any]						  =    int(a				)
			return SageMakerDistributedType(["NO", "DATA_PARALLEL", "MODEL_PARALLEL"][value]				)


def 				lowerCamelCase__	(      a	:   Union[str, Any]				)    ->	List[str]:





			"""simple docstring"""
			return {"yes": True, "no": False}[value.lower()]







class 					lowerCAmelCase_ (       argparse.RawDescriptionHelpFormatter):




						def  _snake_case					(	self						:   Tuple   ,     __A						:   Tuple   ,     __A						:   int   ,     __A						:   Tuple   ,     __A						:   Any						)      ->Union[str, Any]:






									"""simple docstring"""






									a__ :Optional[int]						  =    super()._format_usage(__A   ,     __A   ,     __A   ,     __A						)
									a__ :Any						  =    usage.replace("<command> [<args>] "   ,     ""						)
									return usage


