


import math
def   snake_case_    (			__lowercase							):





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





   if n <= 0:
      raise ValueError('''Only positive numbers are accepted'''							)
   UpperCAmelCase_				:   Dict							= 1
   UpperCAmelCase_				:   Any							= 1
   while n % 2 == 0:
      temp += 1
      UpperCAmelCase_				:   Any							= int(n / 2							)
   div *= temp
   for i in range(3      ,							int(math.sqrt(__snake_case							)							) + 1      ,							2							):
      UpperCAmelCase_				:   List[Any]							= 1
      while n % i == 0:
         temp += 1
         UpperCAmelCase_				:   Any							= int(n / i							)
      div *= temp
   if n > 1:
      div *= 2
   return div
def   snake_case_    (			__lowercase							):





   if n <= 0:
      raise ValueError('''Only positive numbers are accepted'''							)
   UpperCAmelCase_				:   str							= 1
   UpperCAmelCase_				:   Any							= 1
   while n % 2 == 0:
      temp += 1
      UpperCAmelCase_				:   Union[str, Any]							= int(n / 2							)
   if temp > 1:
      s *= (2**temp - 1) / (2 - 1)
   for i in range(3      ,							int(math.sqrt(__snake_case							)							) + 1      ,							2							):
      UpperCAmelCase_				:   Tuple							= 1
      while n % i == 0:
         temp += 1
         UpperCAmelCase_				:   Union[str, Any]							= int(n / i							)
      if temp > 1:
         s *= (i**temp - 1) / (i - 1)
   return int(__snake_case							)
def   snake_case_    (			__lowercase							):
   UpperCAmelCase_				:   Optional[int]							= n
   for x in set(prime_factors(__snake_case							)							):
      s *= (x - 1) / x
   return int(__snake_case							)


if __name__ == "__main__":
       import doctest

       doctest.testmod()







"""simple docstring"""



from __future__ import annotations

import random
from collections.abc import Iterable
from typing import Any, Generic, TypeVar

_UpperCamelCase						:    Optional[int]		=						TypeVar('T', bound=bool)

class 			a	(  Generic[T]      ):







    def __init__(     self				,						_lowerCamelCase			):
      lowercase				       =			value
      lowercase				       =			None
      lowercase				       =			None







    @property
    def      UpperCamelCase_ (     self			):
      return self._value







    @staticmethod
    def      UpperCamelCase_ (     _lowerCamelCase				,						_lowerCamelCase			):
      if not roota:
        return roota

      if not roota:
        return roota

      if roota.value > roota.value:
        lowercase       ,	lowercase				       =			roota, roota

      if random.choice([True, False]			):
        lowercase       ,	lowercase				       =			roota.right, roota.left

      lowercase				       =			RandomizedHeapNode.merge(roota.left				,						_lowerCamelCase			)

      return roota


class 			a	(  Generic[T]      ):







    def __init__(     self				,						_lowerCamelCase = ()			):
      lowercase				       =			None

      if data:
        for item in data:
          self.insert(_lowerCamelCase			)







    def      UpperCamelCase_ (     self				,						_lowerCamelCase			):
      lowercase				       =			RandomizedHeapNode.merge(self._root				,						RandomizedHeapNode(_lowerCamelCase			)			)







    def      UpperCamelCase_ (     self			):
      lowercase				       =			self.top()

      if self._root is None:
        return None

      lowercase				       =			RandomizedHeapNode.merge(self._root.left				,						self._root.right			)

      return result







    def      UpperCamelCase_ (     self			):
      if not self._root:
        raise IndexError('Can\'t get top element for the empty heap.'			)
      return self._root.value







    def      UpperCamelCase_ (     self			):
      lowercase				       =			None







    def      UpperCamelCase_ (     self			):
      lowercase				       =			[]
      while self:
        result.append(self.pop()			)

      return result







    def __bool__(     self			):
      return self._root is not None


if __name__ == "__main__":
    import doctest

    doctest.testmod()


