'''simple docstring'''




from __future__ import annotations

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

class      lowerCamelCase_     (snake_case__   ):
      '''simple docstring'''

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




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





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

__SCREAMING_SNAKE_CASE	:					Tuple					=  TypeVar("""T""", bound=Comparable)

class      lowerCamelCase_     (Generic[T]   ):
      '''simple docstring'''

      def __init__(	self						:    Any	):
             _UpperCAmelCase					:  list[T]											=   []
             _UpperCAmelCase					:  int											=   0




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




      def 					_A     (	self						:    int						, A						:    int	):
             if child_idx > 0:
                    return (child_idx - 1) // 2
             return None




      def 					_A     (	self						:    List[str]						, A						:    int	):
             _UpperCAmelCase					:  Optional[Any]											=   2 * parent_idx + 1
             if left_child_index < self.heap_size:
                    return left_child_index
             return None




      def 					_A     (	self						:    List[Any]						, A						:    int	):
             _UpperCAmelCase					:  Tuple											=   2 * parent_idx + 2
             if right_child_index < self.heap_size:
                    return right_child_index
             return None




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




      def 					_A     (	self						:    List[str]						, A						:    Iterable[T]	):
             _UpperCAmelCase					:  Dict											=   list(A	)
             _UpperCAmelCase					:  List[str]											=   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(A	)




      def 					_A     (	self						:    Tuple	):
             if self.heap_size >= 2:
                    _UpperCAmelCase					:  Tuple											=   self.h[0]
                    _UpperCAmelCase					:  Any											=   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 					_A     (	self						:    List[Any]						, A						:    T	):
             self.h.append(A	)
             _UpperCAmelCase					:  Optional[Any]											=   (self.heap_size - 1) // 2
             self.heap_size += 1
             while idx >= 0:
                    self.max_heapify(A	)
                    _UpperCAmelCase					:  str											=   (idx - 1) // 2





      def 					_A     (	self						:    Tuple	):
             _UpperCAmelCase					:  Tuple											=   self.heap_size
             for j in range(size - 1						, 0						, -1	):
                    _UpperCAmelCase				,  _UpperCAmelCase					:  Optional[int]											=   self.h[j], self.h[0]
                    self.heap_size -= 1
                    self.max_heapify(0	)
             _UpperCAmelCase					:  List[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}')

    __SCREAMING_SNAKE_CASE	:					Heap[int]					=  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')


'''simple docstring'''




from __future__ import annotations

from collections.abc import Generator

def      UpperCamelCase_							( _UpperCAmelCase  :				int   )   ->   Generator[int, None, None]:


       """simple docstring"""







       if not isinstance(_UpperCAmelCase      ,     _UpperCAmelCase   ) or n < 1:
              raise Exception("Sequence only defined for positive integers"   )

       yield n
       while n != 1:
              if n % 2 == 0:
                     n //= 2
              else:
                     _UpperCAmelCase					:  Optional[Any]											=   3 * n + 1
              yield n

def      UpperCamelCase_							( )   ->   Any:


       """simple docstring"""







       _UpperCAmelCase					:  str											=   43
       _UpperCAmelCase					:  Optional[int]											=   tuple(collatz_sequence(_UpperCAmelCase   )   )
       print(_UpperCAmelCase   )
       print(F"""Collatz sequence from {n} took {len(_UpperCAmelCase   )} steps."""   )


if __name__ == "__main__":
  main()

