




def lowerCamelCase__  (     _lowercase					,		_lowercase ):

     '''simple docstring'''


     if density <= 0:
          raise ValueError('''Impossible fluid density''' )
     if bulk_modulus <= 0:
          raise ValueError('''Impossible bulk modulus''' )

     return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
     import doctest

     doctest.testmod()

"""simple docstring"""

from math import ceil, sqrt




def      lowercase__    (       lowerCAmelCase					:       int = 1_000_000			)			->   int:






    """simple docstring"""




    UpperCAmelCase          =       0

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



