


from typing import TYPE_CHECKING

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


UpperCamelCase__											= {
    "configuration_audio_spectrogram_transformer": [
        "AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "ASTConfig",
    ]
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase__											= [
					    "AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
					    "ASTForAudioClassification",
					    "ASTModel",
					    "ASTPreTrainedModel",
					]

try:
					if not is_speech_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase__											= ["ASTFeatureExtractor"]

if TYPE_CHECKING:
					from .configuration_audio_spectrogram_transformer import (
					    AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    ASTConfig,
					)

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_audio_spectrogram_transformer import (
										    AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
										    ASTForAudioClassification,
										    ASTModel,
										    ASTPreTrainedModel,
										)

					try:
										if not is_speech_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .feature_extraction_audio_spectrogram_transformer import ASTFeatureExtractor


else:
					import sys

					UpperCamelCase__											= _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)











from math import ceil, sqrt





def     _UpperCamelCase     (a__   :int = 100_0000       ):






							"""simple docstring"""





							UpperCamelCase__				     =			0

							for outer_width in range(3   ,			(limit // 4) + 2       ):
														if outer_width**2 > limit:
																					UpperCamelCase__				     =			max(ceil(sqrt(outer_width**2 - limit       )       )   ,			1       )
														else:
																					UpperCamelCase__				     =			1
														if (outer_width - hole_width_lower_bound) % 2:
																					hole_width_lower_bound += 1

														answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

							return answer


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




