
'''simple docstring'''
import math







def 		A_(     A						:		int):
							UpperCamelCase   			=     math.loga(math.sqrt(4 * positive_integer + 1) / 2 + 1 / 2)

							return exponent == int(A)







def 		A_(     A						:		float = 1 / 1_2345):
							UpperCamelCase   			=     0
							UpperCamelCase   			=     0

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


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






'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


lowerCAmelCase					:    Optional[Any]           = {
    'configuration_falcon': ['FALCON_PRETRAINED_CONFIG_ARCHIVE_MAP', 'FalconConfig'],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase					:    str           = [
						    'FALCON_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'FalconForCausalLM',
						    'FalconModel',
						    'FalconPreTrainedModel',
						    'FalconForSequenceClassification',
						    'FalconForTokenClassification',
						    'FalconForQuestionAnswering',
						]


if TYPE_CHECKING:
						from .configuration_falcon import FALCON_PRETRAINED_CONFIG_ARCHIVE_MAP, FalconConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_falcon import (
												    FALCON_PRETRAINED_MODEL_ARCHIVE_LIST,
												    FalconForCausalLM,
												    FalconForQuestionAnswering,
												    FalconForSequenceClassification,
												    FalconForTokenClassification,
												    FalconModel,
												    FalconPreTrainedModel,
												)


else:
						import sys

						lowerCAmelCase					:    Tuple           = _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




