





'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowercase__   :				Any      =   {
    '''configuration_git''': ['''GIT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''GitConfig''', '''GitVisionConfig'''],
    '''processing_git''': ['''GitProcessor'''],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowercase__   :				List[Any]      =   [
      '''GIT_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''GitForCausalLM''',
      '''GitModel''',
      '''GitPreTrainedModel''',
      '''GitVisionModel''',
  ]

if TYPE_CHECKING:
  from .configuration_git import GIT_PRETRAINED_CONFIG_ARCHIVE_MAP, GitConfig, GitVisionConfig
  from .processing_git import GitProcessor

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_git import (
        GIT_PRETRAINED_MODEL_ARCHIVE_LIST,
        GitForCausalLM,
        GitModel,
        GitPreTrainedModel,
        GitVisionModel,
    )

else:
  import sys

  lowercase__   :				List[str]      =   _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)








'''simple docstring'''




import math






def 	_lowerCAmelCase      (  __snake_case  :			int      )					->					int:

     if not isinstance(__snake_case			,							__snake_case      ):
          __A						:			List[Any]								=	f'Input value of [number={number}] must be an integer'
          raise TypeError(__snake_case      )

     if number < 1:
          __A						:			Union[str, Any]								=	f'Input value of [number={number}] must be > 0'
          raise ValueError(__snake_case      )
     elif number == 1:
          return 3
     elif number == 2:
          return 5
     else:
          __A						:			Optional[Any]								=	int(math.log(number // 3			,							2      )      ) + 2

          __A						:			Union[str, Any]								=	[3, 5]
          __A						:			List[Any]								=	2
          __A						:			Optional[Any]								=	3
          for block in range(1			,							__snake_case      ):
               for _ in range(__snake_case      ):
                    proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]      )
                    proth_index += 1
               increment *= 2

     return proth_list[number - 1]


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  for number in range(11):
    lowercase__   :				str      =   0
    try:
      lowercase__   :				List[str]      =   proth(number)
    except ValueError:
      print(f"""ValueError: there is no {number}th Proth number""")
      continue

    print(f"""The {number}th Proth number: {value}""")