





'''simple docstring'''






import math





def       lowercase_      (		lowercase__						)   ->bool:
						_snake_case:   Union[str, Any]  					=		math.loga(math.sqrt(4 * positive_integer + 1						) / 2 + 1 / 2						)

						return exponent == int(lowercase__						)





def       lowercase_      (		lowercase__ = 1 / 1_2345						)   ->int:
						_snake_case:   Dict  					=		0
						_snake_case:   int  					=		0

						_snake_case:   Optional[int]  					=		3
						while True:
												_snake_case:   List[str]  					=		(integer**2 - 1) / 4
												# if candidate is an integer, then there is a partition for k
												if partition_candidate == int(lowercase__						):
																		_snake_case:   List[str]  					=		int(lowercase__						)
																		total_partitions += 1
																		if check_partition_perfect(lowercase__						):
																								perfect_partitions += 1
												if perfect_partitions > 0:
																		if perfect_partitions / total_partitions < max_proportion:
																								return int(lowercase__						)
												integer += 1


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












'''simple docstring'''






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


A   : Dict             =			{'configuration_speech_encoder_decoder': ['SpeechEncoderDecoderConfig']}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		A   : int             =			['SpeechEncoderDecoderModel']

try:
		if not is_flax_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		A   : Union[str, Any]             =			['FlaxSpeechEncoderDecoderModel']

if TYPE_CHECKING:
		from .configuration_speech_encoder_decoder import SpeechEncoderDecoderConfig

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_speech_encoder_decoder import SpeechEncoderDecoderModel

		try:
				if not is_flax_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_flax_speech_encoder_decoder import FlaxSpeechEncoderDecoderModel

else:
		import sys

		A   : int             =			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)





