from __future__ import annotations
def    __magic_name__(	__UpperCAmelCase		)    ->     list[int]:



      '''simple docstring'''

      _lowerCamelCase           =					[0] * max_one

      for i in range(0			,    SCREAMING_SNAKE_CASE__		):
            _lowerCamelCase           =					i

      for i in range(2			,    SCREAMING_SNAKE_CASE__		):
            if totients[i] == i:
                  for j in range(SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__		):
                        totients[j] -= totients[j] // i

      return totients
def    __magic_name__(	__UpperCAmelCase			,    __UpperCAmelCase		)    ->     bool:



      '''simple docstring'''

      return sorted(str(SCREAMING_SNAKE_CASE__		)		) == sorted(str(SCREAMING_SNAKE_CASE__		)		)
def    __magic_name__(	__UpperCAmelCase = 1000_0000		)    ->     int:



      '''simple docstring'''

      _lowerCamelCase           =					1  # i
      _lowerCamelCase           =					0  # φ(i)
      _lowerCamelCase           =					get_totients(max_n + 1		)

      for i in range(2			,    max_n + 1		):
            _lowerCamelCase           =					totients[i]

            if i * min_denominator < min_numerator * t and has_same_digits(SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__		):
                  _lowerCamelCase           =					i
                  _lowerCamelCase           =					t

      return min_numerator


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,
)


snake_case_  :							Any            =	{
    "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:
					snake_case_  :							str            =	[
					    "DPRContextEncoderTokenizerFast",
					    "DPRQuestionEncoderTokenizerFast",
					    "DPRReaderTokenizerFast",
					]

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					snake_case_  :							Optional[int]            =	[
					    "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:
					snake_case_  :							Dict            =	[
					    "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

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





