
'''simple docstring'''






from typing import TYPE_CHECKING

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


UpperCAmelCase_       :   str   =       {
    'configuration_trocr': ['TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP', 'TrOCRConfig'],
    'processing_trocr': ['TrOCRProcessor'],
}


try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 UpperCAmelCase_       :   List[Any]   =       [
     '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

 UpperCAmelCase_       :   Optional[int]   =       _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


'''simple docstring'''






import math







def 		A_       (	_lowerCAmelCase   :    int							):



      """simple docstring"""




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

      return exponent == int(_lowerCAmelCase							)







def 		A_       (	_lowerCAmelCase   :    float = 1 / 12345							):



      """simple docstring"""




      _lowerCamelCase				:   Optional[int]								=   0
      _lowerCamelCase				:   int								=   0

      _lowerCamelCase				:   List[str]								=   3
      while True:
            _lowerCamelCase				:   List[Any]								=   (integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(_lowerCAmelCase							):
                  _lowerCamelCase				:   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() = }''')