


import math



def  _a			(						__UpperCamelCase ):

     if not isinstance(__UpperCamelCase  ,  __UpperCamelCase ):
          a_    :     Optional[int]										=    F'''Input value of [number={number}] must be an integer'''
          raise TypeError(__UpperCamelCase )

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

          a_    :     Tuple										=    [3, 5]
          a_    :     int										=    2
          a_    :     int										=    3
          for block in range(1  ,  __UpperCamelCase ):
               for _ in range(__UpperCamelCase ):
                    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):
              __lowerCamelCase        =     0
              try:
                     __lowerCamelCase        =     proth(number)
              except ValueError:
                     print(f'''ValueError: there is no {number}th Proth number''')
                     continue

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







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCamelCase        =     {
    '''configuration_pegasus_x''': ['''PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''PegasusXConfig'''],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       __lowerCamelCase        =     [
           '''PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST''',
           '''PegasusXForConditionalGeneration''',
           '''PegasusXModel''',
           '''PegasusXPreTrainedModel''',
       ]


if TYPE_CHECKING:
       from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_pegasus_x import (
                  PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
                  PegasusXForConditionalGeneration,
                  PegasusXModel,
                  PegasusXPreTrainedModel,
              )


else:
       import sys

       __lowerCamelCase        =     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



