






from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar

class        snake_case_				(							lowercase_   ):







   """simple docstring"""



   @abstractmethod
   def __lt__(     self:						T ,							snake_case__:						T						)	->		bool:


       """simple docstring"""



       pass

   @abstractmethod
   def __gt__(     self:						T ,							snake_case__:						T						)	->		bool:


       """simple docstring"""



       pass

   @abstractmethod
   def __eq__(     self:						T ,							snake_case__:						object						)	->		bool:


       """simple docstring"""



       pass






lowerCamelCase					    =	TypeVar('''T''', bound=Comparable)

class        snake_case_				(							Generic[T]   ):







   """simple docstring"""



   def __init__(     self:						int						)	->		None:


       """simple docstring"""



       _lowercase     			=						[]
       _lowercase     			=						0

   def __repr__(     self:						List[str]						)	->		str:


       """simple docstring"""



       return str(self.h						)

   def       SCREAMING_SNAKE_CASE__					(     self:						Optional[int] ,							snake_case__:						int						)	->		int | None:


       """simple docstring"""



       if child_idx > 0:
           return (child_idx - 1) // 2
       return None

   def       SCREAMING_SNAKE_CASE__					(     self:						Dict ,							snake_case__:						int						)	->		int | None:


       """simple docstring"""



       _lowercase     			=						2 * parent_idx + 1
       if left_child_index < self.heap_size:
           return left_child_index
       return None

   def       SCREAMING_SNAKE_CASE__					(     self:						Any ,							snake_case__:						int						)	->		int | None:


       """simple docstring"""



       _lowercase     			=						2 * parent_idx + 2
       if right_child_index < self.heap_size:
           return right_child_index
       return None

   def       SCREAMING_SNAKE_CASE__					(     self:						str ,							snake_case__:						int						)	->		None:


       """simple docstring"""



       if index < self.heap_size:
           _lowercase     			=						index
           _lowercase     			=						self.left_child_idx(snake_case__						)
           _lowercase     			=						self.right_child_idx(snake_case__						)
           # check which child is larger than its parent
           if left_child is not None and self.h[left_child] > self.h[violation]:
               _lowercase     			=						left_child
           if right_child is not None and self.h[right_child] > self.h[violation]:
               _lowercase     			=						right_child
           # if violation indeed exists
           if violation != index:
               # swap to fix the violation
               _lowercase			,     _lowercase     			=						self.h[index], self.h[violation]
               # fix the subsequent violation recursively if any
               self.max_heapify(snake_case__						)

   def       SCREAMING_SNAKE_CASE__					(     self:						int ,							snake_case__:						Iterable[T]						)	->		None:


       """simple docstring"""



       _lowercase     			=						list(snake_case__						)
       _lowercase     			=						len(self.h						)
       if self.heap_size > 1:
           # max_heapify from right to left but exclude leaves (last level)
           for i in range(self.heap_size // 2 - 1 ,							-1 ,							-1						):
               self.max_heapify(snake_case__						)

   def       SCREAMING_SNAKE_CASE__					(     self:						Union[str, Any]						)	->		T:


       """simple docstring"""



       if self.heap_size >= 2:
           _lowercase     			=						self.h[0]
           _lowercase     			=						self.h.pop(-1						)
           self.heap_size -= 1
           self.max_heapify(0						)
           return me
       elif self.heap_size == 1:
           self.heap_size -= 1
           return self.h.pop(-1						)
       else:
           raise Exception('Empty heap'						)

   def       SCREAMING_SNAKE_CASE__					(     self:						List[Any] ,							snake_case__:						T						)	->		None:


       """simple docstring"""



       self.h.append(snake_case__						)
       _lowercase     			=						(self.heap_size - 1) // 2
       self.heap_size += 1
       while idx >= 0:
           self.max_heapify(snake_case__						)
           _lowercase     			=						(idx - 1) // 2

   def       SCREAMING_SNAKE_CASE__					(     self:						Any						)	->		None:


       """simple docstring"""



       _lowercase     			=						self.heap_size
       for j in range(size - 1 ,							0 ,							-1						):
           _lowercase			,     _lowercase     			=						self.h[j], self.h[0]
           self.heap_size -= 1
           self.max_heapify(0						)
       _lowercase     			=						size


if __name__ == "__main__":
   import doctest

   # run doc test
   doctest.testmod()

   # demo
   for unsorted in [
       [0],
       [2],
       [3, 5],
       [5, 3],
       [5, 5],
       [0, 0, 0, 0],
       [1, 1, 1, 1],
       [2, 2, 3, 5],
       [0, 2, 2, 3, 5],
       [2, 5, 3, 0, 2, 3, 0, 3],
       [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
       [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
       [-45, -2, -5],
   ]:
      print(f"unsorted array: {unsorted}")

      lowerCamelCase					    =	Heap()
      heap.build_max_heap(unsorted)
      print(f"after build heap: {heap}")

      print(f"max value: {heap.extract_max()}")
      print(f"after max value removed: {heap}")

      heap.insert(100)
      print(f"after new value 100 inserted: {heap}")

      heap.heap_sort()
      print(f"heap-sorted array: {heap}\n")








import math
def 							UpperCAmelCase   ( _lowercase   ):


    '''simple docstring'''



    _lowercase     			=						math.log(2,   10   ) * number
    _lowercase     			=						round((log_number - int(_lowercase   )),   15   )

    return difference
def 							UpperCAmelCase   ( _lowercase = 678910   ):


    '''simple docstring'''



    _lowercase     			=						90
    _lowercase     			=						0

    _lowercase     			=						math.log(1.23,   10   )
    _lowercase     			=						math.log(1.24,   10   )
    _lowercase     			=						0

    while position < number:
        _lowercase     			=						log_difference(_lowercase   )

        if difference >= upper_limit:
            power_iterator += 93

        elif difference < lower_limit:
            power_iterator += 196

        else:
            _lowercase     			=						power_iterator
            power_iterator += 196
            position += 1

    return previous_power


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   print(f"{solution() = }")
