





from math import ceil, sqrt

def   a_   (			lowerCAmelCase_				:      int = 100_0000     ):
   __lowerCAmelCase							     =     0

   for outer_width in range(3,     (limit // 4) + 2     ):
      if outer_width**2 > limit:
         __lowerCAmelCase							     =     max(ceil(sqrt(outer_width**2 - limit     )     ),     1     )
      else:
         __lowerCAmelCase							     =     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 collections.abc import Sequence

def   a_   (			lowerCAmelCase_				:      Sequence[float],     lowerCAmelCase_				:      bool = False     ):
   if not arr:
      return 0

   __lowerCAmelCase							     =     0 if allow_empty_subarrays else float('-inf'     )
   __lowerCAmelCase							     =     0.0
   for num in arr:
      __lowerCAmelCase							     =     max(0 if allow_empty_subarrays else num,     curr_sum + num     )
      __lowerCAmelCase							     =     max(lowerCAmelCase_,     lowerCAmelCase_     )

   return max_sum


if __name__ == "__main__":
     from doctest import testmod

     testmod()

     _snake_case  :   Optional[Any]						   =  [-2, 1, -3, 4, -1, 2, 1, -5, 4]
     print(F"""{max_subarray_sum(nums) = }""")

