



'''simple docstring'''

from __future__ import annotations

# Define the Gravitational Constant G and the function
__lowerCAmelCase		    =     6.6743e-11  # unit of G : m^3 * kg^-1 * s^-2



def   __lowerCamelCase  (   lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_						)    ->   dict[str, float]:
		_a  :   str				 =							mass_a * mass_a

		if (force, mass_a, mass_a, distance).count(0						) != 1:
				raise ValueError('One and only one argument must be 0'						)
		if force < 0:
				raise ValueError('Gravitational force can not be negative'						)
		if distance < 0:
				raise ValueError('Distance can not be negative'						)
		if mass_a < 0 or mass_a < 0:
				raise ValueError('Mass can not be negative'						)
		if force == 0:
				_a  :   List[Any]				 =							GRAVITATIONAL_CONSTANT * product_of_mass / (distance**2)
				return {"force": force}
		elif mass_a == 0:
				_a  :   Any				 =							(force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
				return {"mass_1": mass_a}
		elif mass_a == 0:
				_a  :   Tuple				 =							(force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
				return {"mass_2": mass_a}
		elif distance == 0:
				_a  :   str				 =							(GRAVITATIONAL_CONSTANT * product_of_mass / (force)) ** 0.5
				return {"distance": distance}
		raise ValueError('One and only one argument must be 0'						)


# Run doctest
if __name__ == "__main__":
							import doctest

							doctest.testmod()









'''simple docstring'''

import math



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   list:
		if n <= 0:
				raise ValueError('Only positive integers have prime factors'						)
		_a  :   Tuple				 =							[]
		while n % 2 == 0:
				pf.append(2						)
				_a  :   str				 =							int(n / 2						)
		for i in range(3		,    int(math.sqrt(lowerCAmelCase_						)						) + 1		,    2						):
				while n % i == 0:
						pf.append(lowerCAmelCase_						)
						_a  :   List[Any]				 =							int(n / i						)
		if n > 2:
				pf.append(lowerCAmelCase_						)
		return pf



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   int:
		if n <= 0:
				raise ValueError('Only positive numbers are accepted'						)
		_a  :   int				 =							1
		_a  :   Union[str, Any]				 =							1
		while n % 2 == 0:
				temp += 1
				_a  :   str				 =							int(n / 2						)
		div *= temp
		for i in range(3		,    int(math.sqrt(lowerCAmelCase_						)						) + 1		,    2						):
				_a  :   List[str]				 =							1
				while n % i == 0:
						temp += 1
						_a  :   List[str]				 =							int(n / i						)
				div *= temp
		if n > 1:
				div *= 2
		return div



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   int:
		if n <= 0:
				raise ValueError('Only positive numbers are accepted'						)
		_a  :   List[str]				 =							1
		_a  :   Union[str, Any]				 =							1
		while n % 2 == 0:
				temp += 1
				_a  :   Tuple				 =							int(n / 2						)
		if temp > 1:
				s *= (2**temp - 1) / (2 - 1)
		for i in range(3		,    int(math.sqrt(lowerCAmelCase_						)						) + 1		,    2						):
				_a  :   str				 =							1
				while n % i == 0:
						temp += 1
						_a  :   Any				 =							int(n / i						)
				if temp > 1:
						s *= (i**temp - 1) / (i - 1)
		return int(lowerCAmelCase_						)



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   int:
		_a  :   Dict				 =							n
		for x in set(prime_factors(lowerCAmelCase_						)						):
				s *= (x - 1) / x
		return int(lowerCAmelCase_						)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




