


snake_case							:	str					      =				[
    (10_00, '''M'''),
    (9_00, '''CM'''),
    (5_00, '''D'''),
    (4_00, '''CD'''),
    (1_00, '''C'''),
    (90, '''XC'''),
    (50, '''L'''),
    (40, '''XL'''),
    (10, '''X'''),
    (9, '''IX'''),
    (5, '''V'''),
    (4, '''IV'''),
    (1, '''I'''),
]






def 							__lowercase       (			__lowerCAmelCase							:    str       ):
							a__					=					{'I': 1, 'V': 5, 'X': 1_0, 'L': 5_0, 'C': 1_0_0, 'D': 5_0_0, 'M': 1_0_0_0}
							a__					=					0
							a__					=					0
							while place < len(__lowerCAmelCase       ):
														if (place + 1 < len(__lowerCAmelCase       )) 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 							__lowercase       (			__lowerCAmelCase							:    int       ):
							a__					=					[]
							for arabic, roman in ROMAN:
														((a__)				, (a__))					=					divmod(__lowerCAmelCase ,   __lowerCAmelCase       )
														result.append(roman * factor       )
														if number == 0:
																					break
							return "".join(__lowerCAmelCase       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()








from collections import defaultdict
from math import ceil, sqrt






def 							__lowercase       (			__lowerCAmelCase							:    int = 1_0_0_0_0_0_0 ,   __lowerCAmelCase							:    int = 1_0       ):
							a__					=					defaultdict(__lowerCAmelCase       )

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

														hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

														for hole_width in range(__lowerCAmelCase ,   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 <= 1_0       )


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




