


'''simple docstring'''





class     lowercase__  :






  def __init__(					self      :					Tuple		,						_lowercase      :					Dict		,						_lowercase      :					str ):




         """simple docstring"""







         UpperCAmelCase__										=     name
         UpperCAmelCase__										=     val






  def __str__(					self      :					Dict ):




         """simple docstring"""







         return F"""{self.__class__.__name__}({self.name}, {self.val})"""






  def __lt__(					self      :					Dict		,						_lowercase      :					Optional[Any] ):




         """simple docstring"""







         return self.val < other.val




class     lowercase__  :






  def __init__(					self      :					int		,						_lowercase      :					List[Any] ):




         """simple docstring"""







         UpperCAmelCase__										=     {}
         UpperCAmelCase__										=     {}
         UpperCAmelCase__										=     self.build_heap(_lowercase )






  def __getitem__(					self      :					Any		,						_lowercase      :					Tuple ):




         """simple docstring"""







         return self.get_value(_lowercase )






  def 			_UpperCAmelCase  (					self      :					Optional[int]		,						_lowercase      :					Any ):




         """simple docstring"""







         return (idx - 1) // 2






  def 			_UpperCAmelCase  (					self      :					str		,						_lowercase      :					Union[str, Any] ):




         """simple docstring"""







         return idx * 2 + 1






  def 			_UpperCAmelCase  (					self      :					List[str]		,						_lowercase      :					str ):




         """simple docstring"""







         return idx * 2 + 2






  def 			_UpperCAmelCase  (					self      :					Optional[Any]		,						_lowercase      :					Optional[Any] ):




         """simple docstring"""







         return self.heap_dict[key]






  def 			_UpperCAmelCase  (					self      :					List[Any]		,						_lowercase      :					Tuple ):




         """simple docstring"""







         UpperCAmelCase__										=     len(_lowercase ) - 1
         UpperCAmelCase__										=     self.get_parent_idx(_lowercase )

         for idx, i in enumerate(_lowercase ):
                UpperCAmelCase__										=     idx
                UpperCAmelCase__										=     i.val

         for i in range(_lowercase		,						-1		,						-1 ):
                self.sift_down(_lowercase		,						_lowercase )
         return array






  def 			_UpperCAmelCase  (					self      :					str		,						_lowercase      :					Optional[Any]		,						_lowercase      :					Union[str, Any] ):




         """simple docstring"""







         while True:
                UpperCAmelCase__										=     self.get_left_child_idx(_lowercase )  # noqa: E741
                UpperCAmelCase__										=     self.get_right_child_idx(_lowercase )

                UpperCAmelCase__										=     idx
                if l < len(_lowercase ) and array[l] < array[idx]:
                       UpperCAmelCase__										=     l
                if r < len(_lowercase ) and array[r] < array[smallest]:
                       UpperCAmelCase__										=     r

                if smallest != idx:
                       UpperCAmelCase__						,			UpperCAmelCase__										=     array[smallest], array[idx]
                       (
                           (
                           UpperCAmelCase__			
                       )						,			(
                           UpperCAmelCase__			
                       )						,						
                       )										=     (
                           self.idx_of_element[array[smallest]],
                           self.idx_of_element[array[idx]],
                       )
                       UpperCAmelCase__										=     smallest
                else:
                       break






  def 			_UpperCAmelCase  (					self      :					List[str]		,						_lowercase      :					Tuple ):




         """simple docstring"""







         UpperCAmelCase__										=     self.get_parent_idx(_lowercase )
         while p >= 0 and self.heap[p] > self.heap[idx]:
                UpperCAmelCase__						,			UpperCAmelCase__										=     self.heap[idx], self.heap[p]
                UpperCAmelCase__						,			UpperCAmelCase__										=     (
                    self.idx_of_element[self.heap[idx]],
                    self.idx_of_element[self.heap[p]],
                )
                UpperCAmelCase__										=     p
                UpperCAmelCase__										=     self.get_parent_idx(_lowercase )






  def 			_UpperCAmelCase  (					self      :					str ):




         """simple docstring"""







         return self.heap[0]






  def 			_UpperCAmelCase  (					self      :					List[Any] ):




         """simple docstring"""







         UpperCAmelCase__						,			UpperCAmelCase__										=     self.heap[-1], self.heap[0]
         UpperCAmelCase__						,			UpperCAmelCase__										=     (
             self.idx_of_element[self.heap[-1]],
             self.idx_of_element[self.heap[0]],
         )

         UpperCAmelCase__										=     self.heap.pop()
         del self.idx_of_element[x]
         self.sift_down(0		,						self.heap )
         return x






  def 			_UpperCAmelCase  (					self      :					Any		,						_lowercase      :					Any ):




         """simple docstring"""







         self.heap.append(_lowercase )
         UpperCAmelCase__										=     len(self.heap ) - 1
         UpperCAmelCase__										=     node.val
         self.sift_up(len(self.heap ) - 1 )






  def 			_UpperCAmelCase  (					self      :					Tuple ):




         """simple docstring"""







         return len(self.heap ) == 0






  def 			_UpperCAmelCase  (					self      :					List[str]		,						_lowercase      :					Union[str, Any]		,						_lowercase      :					Union[str, Any] ):




         """simple docstring"""







         assert (
             self.heap[self.idx_of_element[node]].val > new_value
         ), "newValue must be less that current value"
         UpperCAmelCase__										=     new_value
         UpperCAmelCase__										=     new_value
         self.sift_up(self.idx_of_element[node] )




A      = Node("R", -1)
A      = Node("B", 6)
A      = Node("A", 3)
A      = Node("X", 1)
A      = Node("E", 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
A      = MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print("Min Heap - before decrease key")
for i in my_min_heap.heap:
    print(i)

print("Min Heap - After decrease key of node [B -> -17]")
my_min_heap.decrease_key(b, -17)

# After
for i in my_min_heap.heap:
    print(i)

if __name__ == "__main__":
    import doctest

    doctest.testmod()









from __future__ import annotations





def __UpperCAmelCase       (		__A			)						->					list[int]:



       '''simple docstring'''





       UpperCAmelCase__										=     [True] * limit
       UpperCAmelCase__										=     False
       UpperCAmelCase__										=     False
       UpperCAmelCase__										=     True

       for i in range(3 ,						int(limit**0.5 + 1			) ,						2			):
              UpperCAmelCase__										=     i * 2
              while index < limit:
                     UpperCAmelCase__										=     False
                     UpperCAmelCase__										=     index + i

       UpperCAmelCase__										=     [2]

       for i in range(3 ,						__A ,						2			):
              if is_prime[i]:
                     primes.append(__A			)

       return primes





def __UpperCAmelCase       (		__A = 1_0_0_0_0_0_0			)						->					int:



       '''simple docstring'''





       UpperCAmelCase__										=     prime_sieve(__A			)
       UpperCAmelCase__										=     0
       UpperCAmelCase__										=     0

       for i in range(len(__A			)			):
              for j in range(i + length ,						len(__A			)			):
                     UpperCAmelCase__										=     sum(primes[i:j]			)
                     if sol >= ceiling:
                            break

                     if sol in primes:
                            UpperCAmelCase__										=     j - i
                            UpperCAmelCase__										=     sol

       return largest


if __name__ == "__main__":
    print(f"{solution() = }")





