


import math



def 			lowerCAmelCase (		lowerCAmelCase_ )-> bool:

				if 1 < number < 4:
								# 2 and 3 are primes
								return True
				elif number < 2 or number % 2 == 0 or number % 3 == 0:
								# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
								return False

				# All primes number are in format of 6k +/- 1
				for i in range(5 ,   int(math.sqrt(lowerCAmelCase_ ) + 1 ) ,   6 ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True



def 			lowerCAmelCase (		lowerCAmelCase_ = 0.1 )-> int:
				lowerCAmelCase_ :      Tuple    				=				3
				lowerCAmelCase_ :      Dict    				=				3

				while primes / (2 * j - 1) >= ratio:
								for i in range(j * j + j + 1 ,   (j + 2) * (j + 2) ,   j + 1 ):
												primes += is_prime(lowerCAmelCase_ )
								j += 2
				return j


if __name__ == "__main__":
	import doctest

	doctest.testmod()



_UpperCAmelCase			:  Dict     =[
    (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 (		lowerCAmelCase_ )-> int:
				lowerCAmelCase_ :      Any    				=				{'''I''': 1, '''V''': 5, '''X''': 10, '''L''': 50, '''C''': 100, '''D''': 500, '''M''': 1_000}
				lowerCAmelCase_ :      Optional[int]    				=				0
				lowerCAmelCase_ :      List[str]    				=				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 			lowerCAmelCase (		lowerCAmelCase_ )-> str:
				lowerCAmelCase_ :      List[Any]    				=				[]
				for arabic, roman in ROMAN:
								((lowerCAmelCase_)				,  (lowerCAmelCase_)) :      Optional[int]    				=				divmod(lowerCAmelCase_ ,   lowerCAmelCase_ )
								result.append(roman * factor )
								if number == 0:
												break
				return "".join(lowerCAmelCase_ )


if __name__ == "__main__":
						import doctest

						doctest.testmod()