





"""simple docstring"""


from __future__ import annotations

from typing import Generic, TypeVar

a__   :       Optional[Any]   						=			TypeVar("""T""")



class        lowercase_			(       __lowerCAmelCase							):
       pass



class        lowercase_			(       __lowerCAmelCase							):
       pass



class        lowercase_			(       Generic[T]							):

       def __init__(     self				,   __SCREAMING_SNAKE_CASE = 10       ):






        '''simple docstring'''

        snake_case__      							=			[]
        snake_case__      							=			limit

       def __bool__(     self       ):






        '''simple docstring'''

        return bool(self.stack       )

       def __str__(     self       ):






        '''simple docstring'''

        return str(self.stack       )

       def 						_SCREAMING_SNAKE_CASE(     self				,   __SCREAMING_SNAKE_CASE       ):






        '''simple docstring'''

        if len(self.stack       ) >= self.limit:
         raise StackOverflowError
        self.stack.append(__SCREAMING_SNAKE_CASE       )

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        if not self.stack:
         raise StackUnderflowError
        return self.stack.pop()

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        if not self.stack:
         raise StackUnderflowError
        return self.stack[-1]

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        return not bool(self.stack       )

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        return self.size() == self.limit

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        return len(self.stack       )

       def __contains__(     self				,   __SCREAMING_SNAKE_CASE       ):






        '''simple docstring'''

        return item in self.stack





def 							a__     (					)      ->					None:

 '''simple docstring'''






 snake_case__      							=			Stack(1_0		)
 assert bool(_UpperCAmelCase		) is False
 assert stack.is_empty() is True
 assert stack.is_full() is False
 assert str(_UpperCAmelCase		) == "[]"

 try:
  snake_case__      							=			stack.pop()
  raise AssertionError  # This should not happen
 except StackUnderflowError:
  assert True  # This should happen

 try:
  snake_case__      							=			stack.peek()
  raise AssertionError  # This should not happen
 except StackUnderflowError:
  assert True  # This should happen

 for i in range(1_0		):
  assert stack.size() == i
  stack.push(_UpperCAmelCase		)

 assert bool(_UpperCAmelCase		)
 assert not stack.is_empty()
 assert stack.is_full()
 assert str(_UpperCAmelCase		) == str(list(range(1_0		)		)		)
 assert stack.pop() == 9
 assert stack.peek() == 8

 stack.push(1_0_0		)
 assert str(_UpperCAmelCase		) == str([0, 1, 2, 3, 4, 5, 6, 7, 8, 1_0_0]		)

 try:
  stack.push(2_0_0		)
  raise AssertionError  # This should not happen
 except StackOverflowError:
  assert True  # This should happen

 assert not stack.is_empty()
 assert stack.size() == 1_0

 assert 5 in stack
 assert 5_5 not in stack


if __name__ == "__main__":
   test_stack()








"""simple docstring"""


import math





def 							a__     (					_UpperCAmelCase		)      ->					list:

 '''simple docstring'''






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





def 							a__     (					_UpperCAmelCase		)      ->					int:

 '''simple docstring'''






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





def 							a__     (					_UpperCAmelCase		)      ->					int:

 '''simple docstring'''






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





def 							a__     (					_UpperCAmelCase		)      ->					int:

 '''simple docstring'''






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


if __name__ == "__main__":
   import doctest

   doctest.testmod()

