
import math







def 				A__    (  lowerCamelCase  )     ->		Any:
				UpperCamelCase_:							List[str]		=  0
				if n % 2 == 0:
								count += 1
								while n % 2 == 0:
												UpperCamelCase_:							Dict		=  int(n / 2  )
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

				UpperCamelCase_:							Optional[Any]		=  3

				while i <= int(math.sqrt(lowerCamelCase  )  ):
								if n % i == 0:
												count += 1
												while n % i == 0:
																UpperCamelCase_:							Tuple		=  int(n / i  )
								UpperCamelCase_:							Union[str, Any]		=  i + 2

				# this condition checks the prime
				# number n is greater than 2

				if n > 2:
								count += 1
				return count


if __name__ == "__main__":
							lowerCamelCase_  :       Optional[Any]					      =     51_24_21_83
							print(F"""The number of distinct prime factors is/are {exact_prime_factor_count(n)}""")
							print(F"""The value of log(log(n)) is {math.log(math.log(n)):.4f}""")








from math import cos, sin







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_:							int		=  float(lowerCamelCase  )
				return [[scaling_factor * int(x == y  ) for x in range(2  )] for y in range(2  )]







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_,      UpperCamelCase_:							Union[str, Any]		=  cos(lowerCamelCase  ), sin(lowerCamelCase  )
				return [[c, -s], [s, c]]







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_,      UpperCamelCase_:							Any		=  cos(lowerCamelCase  ), sin(lowerCamelCase  )
				UpperCamelCase_:							List[Any]		=  c * s
				return [[c * c, cs], [cs, s * s]]







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_,      UpperCamelCase_:							List[str]		=  cos(lowerCamelCase  ), sin(lowerCamelCase  )
				UpperCamelCase_:							int		=  c * s
				return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"""    {scaling(5) = }""")
print(F"""  {rotation(45) = }""")
print(F"""{projection(45) = }""")





print(F"""{reflection(45) = }""")






