


'''simple docstring'''




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,
)


_a   :   Optional[Any]												=   {"configuration_xglm": ["XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP", "XGLMConfig"]}

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

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _a   :   Dict												=   ["XGLMTokenizerFast"]

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _a   :   Optional[int]												=   [
           "XGLM_PRETRAINED_MODEL_ARCHIVE_LIST",
           "XGLMForCausalLM",
           "XGLMModel",
           "XGLMPreTrainedModel",
       ]


try:
       if not is_flax_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _a   :   int												=   [
           "FlaxXGLMForCausalLM",
           "FlaxXGLMModel",
           "FlaxXGLMPreTrainedModel",
       ]


try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _a   :   Dict												=   [
           "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

       _a   :   List[Any]												=   _LazyModule(__name__, globals()["__file__"], _import_structure)






from math import ceil, sqrt
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int = 1_0_0_0_0_0_0				)			->						int:
       SCREAMING_SNAKE_CASE_							:				List[Any]		=0

       for outer_width in range(3			,							(limit // 4) + 2				):
              if outer_width**2 > limit:
                     SCREAMING_SNAKE_CASE_							:				List[str]		=max(ceil(sqrt(outer_width**2 - limit				)				)			,							1				)
              else:
                     SCREAMING_SNAKE_CASE_							:				List[str]		=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() = }")
