




import math
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    if n <= 0:
        raise ValueError("""Only positive integers have prime factors"""		)
    a__  			=							[]
    while n % 2 == 0:
        pf.append(2		)
        a__  			=							int(n / 2		)
    for i in range(3 ,     int(math.sqrt(UpperCAmelCase_		)		) + 1 ,     2		):
        while n % i == 0:
            pf.append(UpperCAmelCase_		)
            a__  			=							int(n / i		)
    if n > 2:
        pf.append(UpperCAmelCase_		)
    return pf
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    if n <= 0:
        raise ValueError("""Only positive numbers are accepted"""		)
    a__  			=							1
    a__  			=							1
    while n % 2 == 0:
        temp += 1
        a__  			=							int(n / 2		)
    div *= temp
    for i in range(3 ,     int(math.sqrt(UpperCAmelCase_		)		) + 1 ,     2		):
        a__  			=							1
        while n % i == 0:
            temp += 1
            a__  			=							int(n / i		)
        div *= temp
    if n > 1:
        div *= 2
    return div
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    if n <= 0:
        raise ValueError("""Only positive numbers are accepted"""		)
    a__  			=							1
    a__  			=							1
    while n % 2 == 0:
        temp += 1
        a__  			=							int(n / 2		)
    if temp > 1:
        s *= (2**temp - 1) / (2 - 1)
    for i in range(3 ,     int(math.sqrt(UpperCAmelCase_		)		) + 1 ,     2		):
        a__  			=							1
        while n % i == 0:
            temp += 1
            a__  			=							int(n / i		)
        if temp > 1:
            s *= (i**temp - 1) / (i - 1)
    return int(UpperCAmelCase_		)
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    a__  			=							n
    for x in set(prime_factors(UpperCAmelCase_		)		):
        s *= (x - 1) / x
    return int(UpperCAmelCase_		)


if __name__ == "__main__":
 import doctest

 doctest.testmod()












from __future__ import annotations

from typing import Generic, TypeVar

SCREAMING_SNAKE_CASE_    :       List[str]       =							TypeVar('''T''')







class 		__UpperCAmelCase(		lowercase__			):





     """simple docstring"""



     pass







class 		__UpperCAmelCase(		lowercase__			):





     """simple docstring"""



     pass







class 		__UpperCAmelCase(		Generic[T]			):





     """simple docstring"""



     def __init__(   self			:							str    ,					A			:							int = 10     )      ->      str:






         """simple docstring"""
         a__  			=							[]
         a__  			=							limit

     def __bool__(   self			:							Dict     )      ->      bool:






         """simple docstring"""
         return bool(self.stack     )

     def __str__(   self			:							str     )      ->      str:






         """simple docstring"""
         return str(self.stack     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							List[str]    ,					A			:							T     )      ->      None:






         """simple docstring"""
         if len(self.stack     ) >= self.limit:
             raise StackOverflowError
         self.stack.append(A     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Any     )      ->      T:






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

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Optional[int]     )      ->      T:






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

     def 					__SCREAMING_SNAKE_CASE		(   self			:							str     )      ->      bool:






         """simple docstring"""
         return not bool(self.stack     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Dict     )      ->      bool:






         """simple docstring"""
         return self.size() == self.limit

     def 					__SCREAMING_SNAKE_CASE		(   self			:							int     )      ->      int:






         """simple docstring"""
         return len(self.stack     )






     def __contains__(   self			:							int    ,					A			:							T     )      ->      bool:






         """simple docstring"""
         return item in self.stack






def 							__lowerCAmelCase			():
    a__  			=							Stack(10		)
    assert bool(UpperCAmelCase_		) is False
    assert stack.is_empty() is True
    assert stack.is_full() is False
    assert str(UpperCAmelCase_		) == "[]"

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

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

    for i in range(10		):
        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(10		)		)		)
    assert stack.pop() == 9
    assert stack.peek() == 8

    stack.push(100		)
    assert str(UpperCAmelCase_		) == str([0, 1, 2, 3, 4, 5, 6, 7, 8, 100]		)

    try:
        stack.push(200		)
        raise AssertionError  # This should not happen
    except StackOverflowError:
        assert True  # This should happen

    assert not stack.is_empty()
    assert stack.size() == 10

    assert 5 in stack
    assert 55 not in stack


if __name__ == "__main__":
 test_stack()






