



from collections import defaultdict
from math import ceil, sqrt

def      lowerCAmelCase_					(  _lowercase    :       int = 100_0000						,       _lowercase    :       int = 10)							->	int:







			"""simple docstring"""
			a__       :						defaultdict							=  defaultdict(_lowercase)

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

						hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

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











_lowercase		:				Optional[int]      		=[
    (1000, "M"),
    (900, "CM"),
    (500, "D"),
    (400, "CD"),
    (100, "C"),
    (90, "XC"),
    (50, "L"),
    (40, "XL"),
    (10, "X"),
    (9, "IX"),
    (5, "V"),
    (4, "IV"),
    (1, "I"),
]

def      lowerCAmelCase_					(  _lowercase    :       str)							->	int:







			"""simple docstring"""
			a__       :						Union[str, Any]							=  {"""I""": 1, """V""": 5, """X""": 10, """L""": 50, """C""": 100, """D""": 500, """M""": 1000}
			a__       :						List[Any]							=  0
			a__       :						Dict							=  0
			while place < len(_lowercase):
						if (place + 1 < len(_lowercase)) and (vals[roman[place]] < vals[roman[place + 1]]):
									total += vals[roman[place + 1]] - vals[roman[place]]
									place += 2
						else:
									total += vals[roman[place]]
									place += 1
			return total

def      lowerCAmelCase_					(  _lowercase    :       int)							->	str:







			"""simple docstring"""
			a__       :						Optional[Any]							=  []
			for arabic, roman in ROMAN:
						((a__)	,						(a__))       :						Optional[Any]							=  divmod(_lowercase						,       _lowercase)
						result.append(roman * factor)
						if number == 0:
									break
			return "".join(_lowercase)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




