






'''simple docstring'''






import math
from decimal import Decimal, getcontext




def 							_SCREAMING_SNAKE_CASE	(					A	:							int = 4_00_00_00	)     ->			int:







   """simple docstring"""

   try:
      __snake_case					:   Tuple  				=			int(A	)
   except (TypeError, ValueError):
      raise TypeError('Parameter n must be int or castable to int.'	)
   if n <= 0:
      raise ValueError('Parameter n must be greater than or equal to one.'	)
   __snake_case					:   List[str]  				=			1_00
   __snake_case					:   Any  				=			(Decimal(5	) ** Decimal(0.5	) + 1) / Decimal(2	)

   __snake_case					:   Any  				=			(math.floor(math.log(n * (phi + 2)	,		A	) - 1	) // 3) * 3 + 2
   __snake_case					:   List[Any]  				=			Decimal(round(phi ** Decimal(index + 1	)	)	) / (phi + 2)
   __snake_case					:   Dict  				=			num // 2
   return int(A	)


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() = }''')