code: 
  
  
  
  
  
  from __future__ import annotations
  
  def     a						(      _lowercase   :     int       )     ->list[int]:
  		UpperCamelCase__         =	[0] * max_one
  
  		for i in range(0 ,						_lowercase       ):
  				UpperCamelCase__         =	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       )     ->bool:
  		return sorted(str(_lowercase       )       ) == sorted(str(_lowercase       )       )
  
  def     a						(      _lowercase   :     int = 1_0_0_0_0_0_0_0       )     ->int:
  		UpperCamelCase__         =	1  # i
  		UpperCamelCase__         =	0  # φ(i)
  		UpperCamelCase__         =	get_totients(max_n + 1       )
  
  		for i in range(2 ,						max_n + 1       ):
  				UpperCamelCase__         =	totients[i]
  
  				if i * min_denominator < min_numerator * t and has_same_digits(_lowercase ,						_lowercase       ):
  						UpperCamelCase__         =	i
  						UpperCamelCase__         =	t
  
  		return min_numerator
  
  
  if __name__ == "__main__":
  				print(f"""{solution() = }""")
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  def     a						(      _lowercase   :     int ,						_lowercase   :     int       )     ->int:
  		UpperCamelCase__         =	1.0
  		for i in range(1 ,						r + 1       ):
  				ret *= (n + 1 - i) / i
  		return round(_lowercase       )
  
  def     a						(      _lowercase   :     int       )     ->int:
  		return choose(8 + n ,						_lowercase       ) + choose(9 + n ,						_lowercase       ) - 1_0
  
  def     a						(      _lowercase   :     int       )     ->int:
  		return sum(non_bouncy_exact(_lowercase       ) for i in range(1 ,						n + 1       )       )
  
  def     a						(      _lowercase   :     int = 1_0_0       )     ->int:
  		return non_bouncy_upto(_lowercase       )
  
  
  if __name__ == "__main__":
  				print(f"""{solution() = }""")
  
  
  
  
  
  