


'''simple docstring'''






from __future__ import annotations

import math
from itertools import permutations






def 						_A					(lowerCAmelCase__	:Any		) ->	bool:




     '''simple docstring'''



     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(lowercase_		) + 1		)					,    6		):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True






def 						_A					(lowerCAmelCase__	:Any = 7		) ->	int:




     '''simple docstring'''



     _a         =				''.join(str(lowercase_		) for i in range(1					,    n + 1		)		)
     _a         =				[int(''.join(lowercase_		)		) for i in permutations(lowercase_					,    lowercase_		)]
     _a         =				[num for num in perm_list if is_prime(lowercase_		)]
     return max(lowercase_		) if pandigitals else 0


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







"""simple docstring"""



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


SCREAMING_SNAKE_CASE							=			{
    "configuration_dpr": ["DPR_PRETRAINED_CONFIG_ARCHIVE_MAP", "DPRConfig"],
    "tokenization_dpr": [
        "DPRContextEncoderTokenizer",
        "DPRQuestionEncoderTokenizer",
        "DPRReaderOutput",
        "DPRReaderTokenizer",
    ],
}


try:
      if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE							=			[
          "DPRContextEncoderTokenizerFast",
          "DPRQuestionEncoderTokenizerFast",
          "DPRReaderTokenizerFast",
      ]

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE							=			[
          "DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST",
          "DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST",
          "DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST",
          "DPRContextEncoder",
          "DPRPretrainedContextEncoder",
          "DPRPreTrainedModel",
          "DPRPretrainedQuestionEncoder",
          "DPRPretrainedReader",
          "DPRQuestionEncoder",
          "DPRReader",
      ]

try:
      if not is_tf_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE							=			[
          "TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST",
          "TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST",
          "TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST",
          "TFDPRContextEncoder",
          "TFDPRPretrainedContextEncoder",
          "TFDPRPretrainedQuestionEncoder",
          "TFDPRPretrainedReader",
          "TFDPRQuestionEncoder",
          "TFDPRReader",
      ]


if TYPE_CHECKING:
      from .configuration_dpr import DPR_PRETRAINED_CONFIG_ARCHIVE_MAP, DPRConfig
      from .tokenization_dpr import (
          DPRContextEncoderTokenizer,
          DPRQuestionEncoderTokenizer,
          DPRReaderOutput,
          DPRReaderTokenizer,
      )

      try:
            if not is_tokenizers_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .tokenization_dpr_fast import (
                DPRContextEncoderTokenizerFast,
                DPRQuestionEncoderTokenizerFast,
                DPRReaderTokenizerFast,
            )

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_dpr import (
                DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
                DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
                DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST,
                DPRContextEncoder,
                DPRPretrainedContextEncoder,
                DPRPreTrainedModel,
                DPRPretrainedQuestionEncoder,
                DPRPretrainedReader,
                DPRQuestionEncoder,
                DPRReader,
            )

      try:
            if not is_tf_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tf_dpr import (
                TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
                TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
                TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST,
                TFDPRContextEncoder,
                TFDPRPretrainedContextEncoder,
                TFDPRPretrainedQuestionEncoder,
                TFDPRPretrainedReader,
                TFDPRQuestionEncoder,
                TFDPRReader,
            )

else:
      import sys

      SCREAMING_SNAKE_CASE							=			_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





