

'''simple docstring'''

import math

def 				__UpperCamelCase							(	lowercase__						:  int ):






     '''simple docstring'''





     if n <= 0:
          raise ValueError('Only positive integers have prime factors' )
     __lowercase					=[]
     while n % 2 == 0:
          pf.append(2 )
          __lowercase					=int(n / 2 )
     for i in range(3,					int(math.sqrt(lowercase__ ) ) + 1,					2 ):
          while n % i == 0:
               pf.append(lowercase__ )
               __lowercase					=int(n / i )
     if n > 2:
          pf.append(lowercase__ )
     return pf

def 				__UpperCamelCase							(	lowercase__						:  int ):






     '''simple docstring'''





     if n <= 0:
          raise ValueError('Only positive numbers are accepted' )
     __lowercase					=1
     __lowercase					=1
     while n % 2 == 0:
          temp += 1
          __lowercase					=int(n / 2 )
     div *= temp
     for i in range(3,					int(math.sqrt(lowercase__ ) ) + 1,					2 ):
          __lowercase					=1
          while n % i == 0:
               temp += 1
               __lowercase					=int(n / i )
          div *= temp
     if n > 1:
          div *= 2
     return div

def 				__UpperCamelCase							(	lowercase__						:  int ):






     '''simple docstring'''





     if n <= 0:
          raise ValueError('Only positive numbers are accepted' )
     __lowercase					=1
     __lowercase					=1
     while n % 2 == 0:
          temp += 1
          __lowercase					=int(n / 2 )
     if temp > 1:
          s *= (2**temp - 1) / (2 - 1)
     for i in range(3,					int(math.sqrt(lowercase__ ) ) + 1,					2 ):
          __lowercase					=1
          while n % i == 0:
               temp += 1
               __lowercase					=int(n / i )
          if temp > 1:
               s *= (i**temp - 1) / (i - 1)
     return int(lowercase__ )

def 				__UpperCamelCase							(	lowercase__						:  int ):






     '''simple docstring'''





     __lowercase					=n
     for x in set(prime_factors(lowercase__ ) ):
          s *= (x - 1) / x
     return int(lowercase__ )


if __name__ == "__main__":
       import doctest

       doctest.testmod()





'''simple docstring'''

from __future__ import annotations

# Define the Gravitational Constant G and the function
UpperCAmelCase				   =  6.6_7_4_3E-1_1  # unit of G : m^3 * kg^-1 * s^-2

def 				__UpperCamelCase							(	lowercase__						:  float,					lowercase__						:  float,					lowercase__						:  float,					lowercase__						:  float ):






     '''simple docstring'''





     __lowercase					=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:
          __lowercase					=GRAVITATIONAL_CONSTANT * product_of_mass / (distance**2)
          return {"force": force}
     elif mass_a == 0:
          __lowercase					=(force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
          return {"mass_1": mass_a}
     elif mass_a == 0:
          __lowercase					=(force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
          return {"mass_2": mass_a}
     elif distance == 0:
          __lowercase					=(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()


