



"""simple docstring"""




import math


def      lowercase__   (	_UpperCAmelCase )   ->	int:






      '''simple docstring'''


      lowercase     :					Optional[Any] 		=      math.loga(math.sqrt(4 * positive_integer + 1 ) / 2 + 1 / 2 )

      return exponent == int(lowerCamelCase__ )


def      lowercase__   (	_UpperCAmelCase = 1 / 1_23_45 )   ->	Any:






      '''simple docstring'''


      lowercase     :					Any 		=      0
      lowercase     :					Optional[Any] 		=      0

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


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,
)


__A				={'''configuration_xglm''': ['''XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''XGLMConfig''']}

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

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

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


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


try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A				=[
			    '''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				=_LazyModule(__name__, globals()['''__file__'''], _import_structure)


