



"""simple docstring"""
A:   Dict								=		8.314_4598

def       _snake_case						(						UpperCamelCase						:		float			,		UpperCamelCase						:		float						):
 if temperature < 0:
  raise Exception("""Temperature cannot be less than 0 K"""						)
 if molar_mass <= 0:
  raise Exception("""Molar mass cannot be less than or equal to 0 kg/mol"""						)
 else:
  return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
      import doctest

      # run doctest
      doctest.testmod()

      # example
      A:   Dict								=		3_0_0
      A:   Dict								=		2_8
      A:   str								=		rms_speed_of_molecule(temperature, molar_mass)
      print(f"""Vrms of Nitrogen gas at 300 K is {vrms} m/s""")





"""simple docstring"""
from collections import defaultdict
from math import ceil, sqrt

def       _snake_case						(						UpperCamelCase						:		int = 1000000			,		UpperCamelCase						:		int = 10						):
 UpperCAmelCase	:					defaultdict	=	defaultdict(UpperCamelCase						)

 for outer_width in range(3			,		(t_limit // 4) + 2						):
  if outer_width * outer_width > t_limit:
   UpperCAmelCase	:					str	=	max(
       ceil(sqrt(outer_width * outer_width - t_limit						)						)			,		1						)
  else:
   UpperCAmelCase	:					Optional[Any]	=	1

  hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

  for hole_width in range(UpperCamelCase			,		outer_width - 1			,		2						):
   count[outer_width * outer_width - hole_width * hole_width] += 1

 return sum(1 for n in count.values() if 1 <= n <= 10						)


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