
'''simple docstring'''







from __future__ import annotations

from math import ceil, floor, sqrt





def    UpperCAmelCase_						(__a :       List[Any] = 2_0_0_0_0_0_0					):






   """simple docstring"""

   _a							:      Tuple     =  [0]
   _a							:      Optional[int]     =  4_2

   for idx in range(1					,      ceil(sqrt(target * 2					) * 1.1					)					):
      triangle_numbers.append(triangle_numbers[-1] + idx					)

   # we want this to be as close as possible to target
   _a							:      Dict     =  0
   # the area corresponding to the grid that gives the product closest to target
   _a							:      int     =  0
   # an estimate of b, using the quadratic formula
   _a							:      str     =  4_2
   # the largest integer less than b_estimate
   _a							:      int     =  4_2
   # the largest integer less than b_estimate
   _a							:      Optional[int]     =  4_2
   # the triangle number corresponding to b_floor
   _a							:      int     =  4_2
   # the triangle number corresponding to b_ceil
   _a							:      str     =  4_2

   for idx_a, triangle_a in enumerate(triangle_numbers[1:]					,      1					):
      _a							:      Dict     =  (-1 + sqrt(1 + 8 * target / triangle_a					)) / 2
      _a							:      str     =  floor(__a					)
      _a							:      Optional[int]     =  ceil(__a					)
      _a							:      str     =  triangle_numbers[b_floor]
      _a							:      List[str]     =  triangle_numbers[b_ceil]

      if abs(target - triangle_b_first_guess * triangle_a					) < abs(
          target - best_product					):
         _a							:      Any     =  triangle_b_first_guess * triangle_a
         _a							:      Any     =  idx_a * b_floor

      if abs(target - triangle_b_second_guess * triangle_a					) < abs(
          target - best_product					):
         _a							:      List[Any]     =  triangle_b_second_guess * triangle_a
         _a							:      List[Any]     =  idx_a * b_ceil

   return area


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




"""simple docstring"""


from math import isqrt






def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   [True] * max_number
  for i in range(2 ,isqrt(max_number - 1		) + 1		):
    if is_prime[i]:
      for j in range(i**2 ,lowercase ,lowercase		):
        _UpperCAmelCase    			=   False

  return [i for i in range(2 ,lowercase		) if is_prime[i]]






def      __UpperCAmelCase       (      lowercase = 10**8		):







  """simple docstring"""
  _UpperCAmelCase    			=   calculate_prime_numbers(max_number // 2		)

  _UpperCAmelCase    			=   0
  _UpperCAmelCase    			=   0
  _UpperCAmelCase    			=   len(lowercase		) - 1
  while left <= right:
    while prime_numbers[left] * prime_numbers[right] >= max_number:
      right -= 1
    semiprimes_count += right - left + 1
    left += 1

  return semiprimes_count


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