






'''simple docstring'''






from itertools import product




def 							_SCREAMING_SNAKE_CASE	(					A	:							int = 15	)     ->			int:







   """simple docstring"""
   __snake_case					:   float  				=			0.0
   __snake_case					:   float
   __snake_case					:   int
   __snake_case					:   int
   __snake_case					:   int
   __snake_case					:   int
   __snake_case					:   tuple[int, ...]

   for series in product(range(2	)	,		repeat=A	):
      __snake_case					:   Optional[Any]  				=			series.count(1	)
      __snake_case					:   List[str]  				=			num_turns - num_blue
      if num_red >= num_blue:
         continue
      __snake_case					:   List[Any]  				=			1.0
      for ind, col in enumerate(A	,		2	):
         if col == 0:
            prob *= (ind - 1) / ind
         else:
            prob *= 1 / ind

      total_prob += prob

   return int(1 / total_prob	)


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







'''simple docstring'''






from math import gcd




def 							_SCREAMING_SNAKE_CASE	(					A	:							int = 1_20_00	)     ->			int:







   """simple docstring"""
   __snake_case					:   Dict  				=			0
   for d in range(max_d + 1	):
      for n in range(d // 3 + 1	,		(d + 1) // 2	):
         if gcd(A	,		A	) == 1:
            fractions_number += 1
   return fractions_number


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