





'''simple docstring'''

from __future__ import annotations

import math

__lowerCamelCase : Any											=			"2020.9.26"
__lowerCamelCase : Optional[Any]											=			"xcodz-dot, cclaus, dhruvmanila"







def 							UpperCAmelCase_    (	lowerCAmelCase_		,							lowerCAmelCase_		,							lowerCAmelCase_		,							lowerCAmelCase_		,							lowerCAmelCase_							):

				"""simple docstring"""






				if not all(isinstance(_UpperCamelCase		,							(float, int)							) for val in locals().values()							):
								lowercase         = f'Input values must either be float or int: {list(locals().values()							)}'
								raise TypeError(_UpperCamelCase							)
				lowercase         = ((x * distance) / (z + distance)) * scale
				lowercase         = ((y * distance) / (z + distance)) * scale
				return projected_x, projected_y







def 							UpperCAmelCase_    (	lowerCAmelCase_		,							lowerCAmelCase_		,							lowerCAmelCase_		,							lowerCAmelCase_		,							lowerCAmelCase_							):

				"""simple docstring"""






				if not isinstance(_UpperCamelCase		,							_UpperCamelCase							):
								raise TypeError("Axis must be a str"							)
				lowercase         = locals()
				del input_variables["axis"]
				if not all(isinstance(_UpperCamelCase		,							(float, int)							) for val in input_variables.values()							):
								lowercase         = (
								    "Input values except axis must either be float or int: "
								    f'{list(input_variables.values()							)}'
								)
								raise TypeError(_UpperCamelCase							)
				lowercase         = (angle % 360) / 450 * 180 / math.pi
				if axis == "z":
								lowercase         = x * math.cos(_UpperCamelCase							) - y * math.sin(_UpperCamelCase							)
								lowercase         = y * math.cos(_UpperCamelCase							) + x * math.sin(_UpperCamelCase							)
								lowercase         = z
				elif axis == "x":
								lowercase         = y * math.cos(_UpperCamelCase							) - z * math.sin(_UpperCamelCase							)
								lowercase         = z * math.cos(_UpperCamelCase							) + y * math.sin(_UpperCamelCase							)
								lowercase         = x
				elif axis == "y":
								lowercase         = x * math.cos(_UpperCamelCase							) - z * math.sin(_UpperCamelCase							)
								lowercase         = z * math.cos(_UpperCamelCase							) + x * math.sin(_UpperCamelCase							)
								lowercase         = y
				else:
								raise ValueError("not a valid axis, choose one of \'x\', \'y\', \'z\'"							)

				return new_x, new_y, new_z


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			print(f"{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }")
			print(f"{rotate(1.0, 2.0, 3.0, 'y', 90.0) = }")







'''simple docstring'''

from functools import lru_cache







def 							UpperCAmelCase_    (	lowerCAmelCase_							):

				"""simple docstring"""






				lowercase         = 2
				lowercase         = set()
				while i * i <= n:
								if n % i:
												i += 1
								else:
												n //= i
												factors.add(lowerCAmelCase_							)
				if n > 1:
								factors.add(lowerCAmelCase_							)
				return factors







@lru_cache
def 							UpperCAmelCase_    (	lowerCAmelCase_							):

				"""simple docstring"""






				return len(unique_prime_factors(lowerCAmelCase_							)							)







def 							UpperCAmelCase_    (	lowerCAmelCase_							):

				"""simple docstring"""






				return len(set(lowerCAmelCase_							)							) in (0, 1)







def 							UpperCAmelCase_    (	lowerCAmelCase_							):

				"""simple docstring"""






				lowercase         = 2

				while True:
								# Increment each value of a generated range
								lowercase         = [base + i for i in range(lowerCAmelCase_							)]

								# Run elements through out unique_prime_factors function
								# Append our target number to the end.
								lowercase         = [upf_len(lowerCAmelCase_							) for x in group]
								checker.append(lowerCAmelCase_							)

								# If all numbers in the list are equal, return the group variable.
								if equality(lowerCAmelCase_							):
												return group

								# Increment our base variable by 1
								base += 1







def 							UpperCAmelCase_    (	lowerCAmelCase_ = 4							):

				"""simple docstring"""






				lowercase         = run(lowerCAmelCase_							)
				return results[0] if len(lowerCAmelCase_							) else None


if __name__ == "__main__":
			print(solution())




