


from collections import defaultdict
from math import ceil, sqrt
def 				UpperCAmelCase_					(							__snake_case = 1000000     ,						__snake_case = 10						)     ->			int:







 """simple docstring"""


 _lowercase							      =defaultdict(__snake_case						)

 for outer_width in range(3     ,						(t_limit // 4) + 2						):
  if outer_width * outer_width > t_limit:
   _lowercase							      =max(
       ceil(sqrt(outer_width * outer_width - t_limit						)						)     ,						1						)
  else:
   _lowercase							      =1

  hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

  for hole_width in range(__snake_case     ,						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() = }''')





UpperCAmelCase__   	=							8.31_44_62  # Unit - J mol-1 K-1
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case						)     ->			float:







 """simple docstring"""


 if moles < 0 or kelvin < 0 or volume < 0:
  raise ValueError('''Invalid inputs. Enter positive value.'''						)
 return moles * kelvin * UNIVERSAL_GAS_CONSTANT / volume
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case						)     ->			float:







 """simple docstring"""


 if moles < 0 or kelvin < 0 or pressure < 0:
  raise ValueError('''Invalid inputs. Enter positive value.'''						)
 return moles * kelvin * UNIVERSAL_GAS_CONSTANT / pressure


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

  testmod()

