

def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int				):





    """simple docstring"""


    if a < b:
        return gcd(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				)
    if a % b == 0:
        return b
    return gcd(_SCREAMING_SNAKE_CASE       ,      a % b				)


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int				):





    """simple docstring"""


    if y == 0:
        return 1
    SCREAMING_SNAKE_CASE_													=  power(_SCREAMING_SNAKE_CASE       ,      y // 2       ,      _SCREAMING_SNAKE_CASE				) % mod
    SCREAMING_SNAKE_CASE_													=  (temp * temp) % mod
    if y % 2 == 1:
        SCREAMING_SNAKE_CASE_													=  (temp * x) % mod
    return temp


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						int				):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_													=  2
    while b < n:
        if gcd(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				) == 1 and power(_SCREAMING_SNAKE_CASE       ,      n - 1       ,      _SCREAMING_SNAKE_CASE				) != 1:
            return False
        b += 1
    return True


if __name__ == "__main__":
       UpperCamelCase__     :					Union[str, Any]								=			int(input("Enter number: ").strip())
       if is_carmichael_number(number):
              print(F'{number} is a Carmichael Number.')
       else:
              print(F'{number} is not a Carmichael Number.')





from typing import TYPE_CHECKING

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


UpperCamelCase__     :					Dict								=			{
    "configuration_donut_swin": ["DONUT_SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP", "DonutSwinConfig"],
    "processing_donut": ["DonutProcessor"],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCamelCase__     :					Optional[int]								=			[
           "DONUT_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST",
           "DonutSwinModel",
           "DonutSwinPreTrainedModel",
       ]

try:
       if not is_vision_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCamelCase__     :					List[Any]								=			["DonutFeatureExtractor"]
       UpperCamelCase__     :					Dict								=			["DonutImageProcessor"]


if TYPE_CHECKING:
       from .configuration_donut_swin import DONUT_SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP, DonutSwinConfig
       from .processing_donut import DonutProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_donut_swin import (
                  DONUT_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST,
                  DonutSwinModel,
                  DonutSwinPreTrainedModel,
              )

       try:
              if not is_vision_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .feature_extraction_donut import DonutFeatureExtractor
              from .image_processing_donut import DonutImageProcessor

else:
       import sys

       UpperCamelCase__     :					Tuple								=			_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


