

import math



def  snake_case_(_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(lowercase__	)	) + 1					,			2	):
    while n % i == 0:
      pf.append(lowercase__	)
      _snake_case		=				int(n / i	)
  if n > 2:
    pf.append(lowercase__	)
  return pf



def  snake_case_(_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(lowercase__	)	) + 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  snake_case_(_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(lowercase__	)	) + 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(lowercase__	)



def  snake_case_(_UpperCamelCase	)				->      int:



  """simple docstring"""






  _snake_case		=				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

from typing import Generic, TypeVar

__UpperCAmelCase 					=    TypeVar('T')




class      _SCREAMING_SNAKE_CASE   (     A__				):
			pass




class      _SCREAMING_SNAKE_CASE   (     A__				):
			pass




class      _SCREAMING_SNAKE_CASE   (     Generic[T]				):






			def __init__(   self			,  __A = 10			)     ->	Optional[int]:
						lowerCAmelCase_       :list[T]     	=    []
						lowerCAmelCase_       :int     	=    limit






			def __bool__(   self			)     ->	bool:
						return bool(self.stack			)






			def __str__(   self			)     ->	str:
						return str(self.stack			)






			def 					__lowerCAmelCase					(   self			,  __A			)     ->	None:
						if len(self.stack			) >= self.limit:
									raise StackOverflowError
						self.stack.append(__A			)






			def 					__lowerCAmelCase					(   self			)     ->	T:
						if not self.stack:
									raise StackUnderflowError
						return self.stack.pop()






			def 					__lowerCAmelCase					(   self			)     ->	T:
						if not self.stack:
									raise StackUnderflowError
						return self.stack[-1]






			def 					__lowerCAmelCase					(   self			)     ->	bool:
						return not bool(self.stack			)






			def 					__lowerCAmelCase					(   self			)     ->	bool:
						return self.size() == self.limit






			def 					__lowerCAmelCase					(   self			)     ->	int:
						return len(self.stack			)






			def __contains__(   self			,  __A			)     ->	bool:
						return item in self.stack






def 		_snake_case			(      )    ->							None:


			'''simple docstring'''





			lowerCAmelCase_       :Stack[int]     	=    Stack(1_0						)
			assert bool(lowercase__						) is False
			assert stack.is_empty() is True
			assert stack.is_full() is False
			assert str(lowercase__						) == "[]"

			try:
						lowerCAmelCase_       :Optional[Any]     	=    stack.pop()
						raise AssertionError  # This should not happen
			except StackUnderflowError:
						assert True  # This should happen

			try:
						lowerCAmelCase_       :Optional[int]     	=    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(lowercase__						)

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

			stack.push(1_0_0						)
			assert str(lowercase__						) == 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()






