


from typing import TYPE_CHECKING

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


_A		:				Optional[int]									=       {
    '''configuration_trocr''': ['''TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''TrOCRConfig'''],
    '''processing_trocr''': ['''TrOCRProcessor'''],
}


try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _A		:				Dict									=       [
       '''TROCR_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''TrOCRForCausalLM''',
       '''TrOCRPreTrainedModel''',
   ]


if TYPE_CHECKING:
   from .configuration_trocr import TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP, TrOCRConfig
   from .processing_trocr import TrOCRProcessor

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_trocr import TROCR_PRETRAINED_MODEL_ARCHIVE_LIST, TrOCRForCausalLM, TrOCRPreTrainedModel

else:
   import sys

   _A		:				Any									=       _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)






import math



def     __lowerCAmelCase						(							snake_case	:    int )       ->							bool:
   __lowerCamelCase:				Dict     =	math.loga(math.sqrt(4 * positive_integer + 1 ) / 2 + 1 / 2 )

   return exponent == int(snake_case )



def     __lowerCAmelCase						(							snake_case	:    float = 1 / 12345 )       ->							int:
   __lowerCamelCase:				str     =	0
   __lowerCamelCase:				Optional[Any]     =	0

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


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


