code: 
  
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  
  
  
  
  def 			a_   (  lowercase__   :int    ):
  			__lowerCamelCase        =			[0] * max_one
  
  			for i in range(0, lowercase__    ):
  						__lowerCamelCase        =			i
  
  			for i in range(2, lowercase__    ):
  						if totients[i] == i:
  									for j in range(lowercase__, lowercase__, lowercase__    ):
  												totients[j] -= totients[j] // i
  
  			return totients
  
  
  
  
  
  def 			a_   (  lowercase__   :int, lowercase__   :int    ):
  			return sorted(str(lowercase__    )    ) == sorted(str(lowercase__    )    )
  
  
  
  
  
  def 			a_   (  lowercase__   :int = 1000_0000    ):
  			__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(lowercase__, lowercase__    ):
  									__lowerCamelCase        =			i
  									__lowerCamelCase        =			t
  
  			return min_numerator
  
  
  if __name__ == "__main__":
  					print(f"""{solution() = }""")
  
  
  
  
  
style_context: 
  
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  import re
  
  
  
  
  
  def 			a_   (  lowercase__   :list[str]    ):
  
  			def alphanum_key(lowercase__   :int    ):
  						return [int(lowercase__    ) if s.isdigit() else s.lower() for s in re.split("""([0-9]+)""", lowercase__    )]
  
  			return sorted(lowercase__, key=lowercase__    )
  
  
  if __name__ == "__main__":
  					import doctest
  
  					doctest.testmod()
  
  
  
  
  