


from math import ceil, sqrt

def 	lowerCAmelCase__			(      a__:		int = 1_0_0_0_0_0_0	)  ->		int:


							'''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() = }''')




from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCAmelCase__  :Any             =							{'''configuration_xglm''': ['''XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''XGLMConfig''']}

try:
		if not is_sentencepiece_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :Optional[Any]             =							['''XGLMTokenizer''']

try:
		if not is_tokenizers_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :str             =							['''XGLMTokenizerFast''']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :List[str]             =							[
		    '''XGLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''XGLMForCausalLM''',
		    '''XGLMModel''',
		    '''XGLMPreTrainedModel''',
		]


try:
		if not is_flax_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :str             =							[
		    '''FlaxXGLMForCausalLM''',
		    '''FlaxXGLMModel''',
		    '''FlaxXGLMPreTrainedModel''',
		]


try:
		if not is_tf_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :List[Any]             =							[
		    '''TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''TFXGLMForCausalLM''',
		    '''TFXGLMModel''',
		    '''TFXGLMPreTrainedModel''',
		]


if TYPE_CHECKING:
		from .configuration_xglm import XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XGLMConfig

		try:
				if not is_sentencepiece_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_xglm import XGLMTokenizer

		try:
				if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_xglm_fast import XGLMTokenizerFast

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_xglm import XGLM_PRETRAINED_MODEL_ARCHIVE_LIST, XGLMForCausalLM, XGLMModel, XGLMPreTrainedModel

		try:
				if not is_flax_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_flax_xglm import FlaxXGLMForCausalLM, FlaxXGLMModel, FlaxXGLMPreTrainedModel

		try:
				if not is_tf_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_tf_xglm import (
				    TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST,
				    TFXGLMForCausalLM,
				    TFXGLMModel,
				    TFXGLMPreTrainedModel,
				)


else:
		import sys

		lowerCAmelCase__  :Any             =							_LazyModule(__name__, globals()['''__file__'''], _import_structure)
