





"""simple docstring"""




from math import ceil, sqrt


def _A       (   __magic_name__ = 100_0000	):
   lowercase__			       =  0

   for outer_width in range(3  , (limit // 4) + 2	):
      if outer_width**2 > limit:
         lowercase__			       =  max(ceil(sqrt(outer_width**2 - limit	)	)  , 1	)
      else:
         lowercase__			       =  1
      if (outer_width - hole_width_lower_bound) % 2:
         hole_width_lower_bound += 1

      answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

   return answer


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













from __future__ import annotations


def _A       (   __magic_name__  , __magic_name__	):
   lowercase__			       =  0
   lowercase__			       =  len(__magic_name__	) - 1

   while i < j:
      if nums[i] + nums[j] == target:
         return [i, j]
      elif nums[i] + nums[j] < target:
         lowercase__			       =  i + 1
      else:
         lowercase__			       =  j - 1

   return []


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(F"""{two_pointer([2, 7, 11, 15], 9) = }""")






