





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


_UpperCAmelCase				       = {
    'configuration_xlm_prophetnet': ['XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP', 'XLMProphetNetConfig'],
}

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

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _UpperCAmelCase				       = [
         'XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST',
         'XLMProphetNetDecoder',
         'XLMProphetNetEncoder',
         'XLMProphetNetForCausalLM',
         'XLMProphetNetForConditionalGeneration',
         'XLMProphetNetModel',
         'XLMProphetNetPreTrainedModel',
     ]


if TYPE_CHECKING:
     from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

     try:
          if not is_sentencepiece_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_xlm_prophetnet import (
              XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
              XLMProphetNetDecoder,
              XLMProphetNetEncoder,
              XLMProphetNetForCausalLM,
              XLMProphetNetForConditionalGeneration,
              XLMProphetNetModel,
              XLMProphetNetPreTrainedModel,
          )

else:
     import sys

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








import math




def        lowerCAmelCase_       (							UpperCamelCase_     )   ->						bool:

       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5    ,						int(math.sqrt(UpperCamelCase_     ) + 1     )    ,						6     ):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True




def        lowerCAmelCase_       (							UpperCamelCase_ = 600851475143     )   ->						int:

       try:
              UpperCamelCase_      				=     int(UpperCamelCase_     )
       except (TypeError, ValueError):
              raise TypeError("Parameter n must be int or castable to int."     )
       if n <= 0:
              raise ValueError("Parameter n must be greater than or equal to one."     )
       UpperCamelCase_      				=     0
       if is_prime(UpperCamelCase_     ):
              return n
       while n % 2 == 0:
              n //= 2
       if is_prime(UpperCamelCase_     ):
              return n
       for i in range(3    ,						int(math.sqrt(UpperCamelCase_     )     ) + 1    ,						2     ):
              if n % i == 0:
                     if is_prime(n // i     ):
                            UpperCamelCase_      				=     n // i
                            break
                     elif is_prime(UpperCamelCase_     ):
                            UpperCamelCase_      				=     i
       return max_number


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

