



"""simple docstring"""




# Lint as: python3

import hashlib
from typing import Union


def 	lowercase__  (      _UpperCAmelCase					)  ->      bytes:






      '''simple docstring'''


      if isinstance(_UpperCAmelCase						,   _UpperCAmelCase					):
            # Data already in bytes, returns as it as
            return hash_data
      elif isinstance(_UpperCAmelCase						,   _UpperCAmelCase					):
            # We keep the data as it as for it ot be later encoded to UTF-8
            # However replace `\\` with `/` for Windows compatibility
            lowercase	:   Optional[int]											= hash_data.replace('\\'						,   '/'					)
      elif isinstance(_UpperCAmelCase						,   _UpperCAmelCase					):
            lowercase	:   int											= str(_UpperCAmelCase					)
      else:
            # If data is not of the required type, raise error
            raise InvalidKeyError(_UpperCAmelCase					)

      return hash_data.encode('utf-8'					)


class 	a__		(    SCREAMING_SNAKE_CASE__  ):


   def __init__(				self   :				int,  lowerCAmelCase   :				Union[str, Any]      )     ->							List[str]:
         lowercase	:   str											= '\nFAILURE TO GENERATE DATASET: Invalid key type detected'
         lowercase	:   Tuple											= f'''\nFound Key {hash_data} of type {type(lowerCAmelCase      )}'''
         lowercase	:   int											= '\nKeys should be either str, int or bytes type'
         super().__init__(f'''{self.prefix}{self.err_msg}{self.suffix}'''      )




class 	a__		(    SCREAMING_SNAKE_CASE__  ):


   def __init__(				self   :				Any,  lowerCAmelCase   :				List[Any],  lowerCAmelCase   :				str,  lowerCAmelCase   :				Tuple=""      )     ->							Dict:
         lowercase	:   List[Any]											= key
         lowercase	:   Optional[int]											= duplicate_key_indices
         lowercase	:   List[str]											= fix_msg
         lowercase	:   Any											= 'Found multiple examples generated with the same key'
         if len(lowerCAmelCase      ) <= 20:
               lowercase	:   List[Any]											= f'''\nThe examples at index {', '.join(lowerCAmelCase      )} have the key {key}'''
         else:
               lowercase	:   List[str]											= f'''\nThe examples at index {', '.join(duplicate_key_indices[:20]      )}... ({len(lowerCAmelCase      ) - 20} more) have the key {key}'''
         lowercase	:   Optional[Any]											= '\n' + fix_msg if fix_msg else ''
         super().__init__(f'''{self.prefix}{self.err_msg}{self.suffix}'''      )




class 	a__		:


   def __init__(				self   :				Optional[int],  lowerCAmelCase   :				str      )     ->							Dict:
         lowercase	:   Any											= hashlib.mda(_as_bytes(lowerCAmelCase      )      )






   def 							lowercase					(				self   :				List[str],  lowerCAmelCase   :				Union[str, int, bytes]      )     ->							int:
         lowercase	:   List[Any]											= self._split_mda.copy()
         lowercase	:   Dict											= _as_bytes(lowerCAmelCase      )
         mda.update(lowerCAmelCase      )
         # Convert to integer with hexadecimal conversion
         return int(mda.hexdigest(),  16      )





"""simple docstring"""




from __future__ import annotations


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      lowercase	:   Optional[Any]											= [0] * max_one

      for i in range(0						,   _UpperCAmelCase					):
            lowercase	:   List[Any]											= i

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

      return totients


def 	lowercase__  (      _UpperCAmelCase						,   _UpperCAmelCase					)  ->      bool:






      '''simple docstring'''


      return sorted(str(_UpperCAmelCase					)					) == sorted(str(_UpperCAmelCase					)					)


def 	lowercase__  (      _UpperCAmelCase = 10_00_00_00					)  ->      int:






      '''simple docstring'''


      lowercase	:   Union[str, Any]											= 1  # i
      lowercase	:   Any											= 0  # φ(i)
      lowercase	:   int											= get_totients(max_n + 1					)

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

            if i * min_denominator < min_numerator * t and has_same_digits(_UpperCAmelCase						,   _UpperCAmelCase					):
                  lowercase	:   List[Any]											= i
                  lowercase	:   Optional[Any]											= t

      return min_numerator


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