


def 			_a      (    __UpperCamelCase			):

     if not isinstance(__UpperCamelCase	,	__UpperCamelCase			) or number < 0:
          raise ValueError("""Input must be a non-negative integer"""			)

     a_     :  Tuple				      =     number & ~(number - 1)
     a_     :  str				      =     0
     while intermediate:
          intermediate >>= 1
          index += 1
     return index - 1


if __name__ == "__main__":
       import doctest

       doctest.testmod(verbose=True)







from __future__ import annotations

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


class 	a__						(    lowerCAmelCase_     ):

       @abstractmethod
       def __lt__( self   :  T   ,				lowerCamelCase_   :  T     ):
            pass

       @abstractmethod
       def __gt__( self   :  T   ,				lowerCamelCase_   :  T     ):
            pass

       @abstractmethod
       def __eq__( self   :  T   ,				lowerCamelCase_   :  object     ):
            pass

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


class 	a__						(    Generic[T]     ):

       def __init__( self   :  Tuple     ):
            a_     :  list[T]				      =     []
            a_     :  int				      =     0

       def __repr__( self   :  Optional[Any]     ):
            return str(self.h     )

       def     UpperCAmelCase( self   :  Dict   ,				lowerCamelCase_   :  int     ):
            if child_idx > 0:
                 return (child_idx - 1) // 2
            return None

       def     UpperCAmelCase( self   :  Any   ,				lowerCamelCase_   :  int     ):
            a_     :  Tuple				      =     2 * parent_idx + 1
            if left_child_index < self.heap_size:
                 return left_child_index
            return None

       def     UpperCAmelCase( self   :  List[Any]   ,				lowerCamelCase_   :  int     ):
            a_     :  List[Any]				      =     2 * parent_idx + 2
            if right_child_index < self.heap_size:
                 return right_child_index
            return None

       def     UpperCAmelCase( self   :  Optional[int]   ,				lowerCamelCase_   :  int     ):
            if index < self.heap_size:
                 a_     :  int				      =     index
                 a_     :  Union[str, Any]				      =     self.left_child_idx(lowerCamelCase_     )
                 a_     :  Optional[int]				      =     self.right_child_idx(lowerCamelCase_     )
                 # check which child is larger than its parent
                 if left_child is not None and self.h[left_child] > self.h[violation]:
                      a_     :  str				      =     left_child
                 if right_child is not None and self.h[right_child] > self.h[violation]:
                      a_     :  List[Any]				      =     right_child
                 # if violation indeed exists
                 if violation != index:
                      # swap to fix the violation
                      a_      ,      a_     :  int				      =     self.h[index], self.h[violation]
                      # fix the subsequent violation recursively if any
                      self.max_heapify(lowerCamelCase_     )

       def     UpperCAmelCase( self   :  List[str]   ,				lowerCamelCase_   :  Iterable[T]     ):
            a_     :  Dict				      =     list(lowerCamelCase_     )
            a_     :  int				      =     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(lowerCamelCase_     )

       def     UpperCAmelCase( self   :  Tuple     ):
            if self.heap_size >= 2:
                 a_     :  int				      =     self.h[0]
                 a_     :  Dict				      =     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     UpperCAmelCase( self   :  List[str]   ,				lowerCamelCase_   :  T     ):
            self.h.append(lowerCamelCase_     )
            a_     :  Optional[int]				      =     (self.heap_size - 1) // 2
            self.heap_size += 1
            while idx >= 0:
                 self.max_heapify(lowerCamelCase_     )
                 a_     :  Union[str, Any]				      =     (idx - 1) // 2

       def     UpperCAmelCase( self   :  int     ):
            a_     :  Union[str, Any]				      =     self.heap_size
            for j in range(size - 1   ,				0   ,				-1     ):
                 a_      ,      a_     :  str				      =     self.h[j], self.h[0]
                 self.heap_size -= 1
                 self.max_heapify(0     )
            a_     :  Union[str, Any]				      =     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''')



