





def _a (  )	->    Any:

							'''simple docstring'''






							for n in range(1			,				1_00_00_00       ):
														yield n * (n + 1) // 2




def _a (  SCREAMING_SNAKE_CASE__      :  Any       )	->    List[str]:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						1
							SCREAMING_SNAKE_CASE__       :      Any     =						2
							while i * i <= n:
														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						0
														while n % i == 0:
																					n //= i
																					multiplicity += 1
														divisors_count *= multiplicity + 1
														i += 1
							if n > 1:
														divisors_count *= 2
							return divisors_count




def _a (  )	->    Optional[int]:

							'''simple docstring'''






							return next(i for i in triangle_number_generator() if count_divisors(SCREAMING_SNAKE_CASE__       ) > 5_00       )


if __name__ == "__main__":
		print(solution())













class 						lowerCamelCase       :







							"""simple docstring"""




							def __init__( self     :					int,			_UpperCAmelCase     :					Dict,			_UpperCAmelCase     :					str						)				->			Optional[Any]:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      str     =						name
														SCREAMING_SNAKE_CASE__       :      Tuple     =						val






							def __str__( self     :					str						)				->			List[Any]:





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






							def __lt__( self     :					str,			_UpperCAmelCase     :					Dict						)				->			Union[str, Any]:





														"""simple docstring"""
														return self.val < other.val


class 						lowerCamelCase       :







							"""simple docstring"""




							def __init__( self     :					Optional[Any],			_UpperCAmelCase     :					str						)				->			Tuple:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      Optional[Any]     =						{}
														SCREAMING_SNAKE_CASE__       :      str     =						{}
														SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						self.build_heap(_UpperCAmelCase						)






							def __getitem__( self     :					Union[str, Any],			_UpperCAmelCase     :					Any						)				->			Dict:





														"""simple docstring"""
														return self.get_value(_UpperCAmelCase						)






							def  A_     ( self     :					int,			_UpperCAmelCase     :					Optional[int]						)				->			Any:





														"""simple docstring"""
														return (idx - 1) // 2






							def  A_     ( self     :					Optional[Any],			_UpperCAmelCase     :					Any						)				->			Dict:





														"""simple docstring"""
														return idx * 2 + 1






							def  A_     ( self     :					str,			_UpperCAmelCase     :					List[str]						)				->			Union[str, Any]:





														"""simple docstring"""
														return idx * 2 + 2






							def  A_     ( self     :					Tuple,			_UpperCAmelCase     :					int						)				->			Optional[int]:





														"""simple docstring"""
														return self.heap_dict[key]






							def  A_     ( self     :					Optional[int],			_UpperCAmelCase     :					Dict						)				->			Optional[Any]:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      List[str]     =						len(_UpperCAmelCase						) - 1
														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						self.get_parent_idx(_UpperCAmelCase						)

														for idx, i in enumerate(_UpperCAmelCase						):
																					SCREAMING_SNAKE_CASE__       :      Optional[int]     =						idx
																					SCREAMING_SNAKE_CASE__       :      Optional[Any]     =						i.val

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






							def  A_     ( self     :					List[Any],			_UpperCAmelCase     :					Dict,			_UpperCAmelCase     :					Tuple						)				->			Tuple:





														"""simple docstring"""
														while True:
																					SCREAMING_SNAKE_CASE__       :      str     =						self.get_left_child_idx(_UpperCAmelCase						)  # noqa: E741
																					SCREAMING_SNAKE_CASE__       :      Tuple     =						self.get_right_child_idx(_UpperCAmelCase						)

																					SCREAMING_SNAKE_CASE__       :      Tuple     =						idx
																					if l < len(_UpperCAmelCase						) and array[l] < array[idx]:
																												SCREAMING_SNAKE_CASE__       :      List[Any]     =						l
																					if r < len(_UpperCAmelCase						) and array[r] < array[smallest]:
																												SCREAMING_SNAKE_CASE__       :      int     =						r

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






							def  A_     ( self     :					Union[str, Any],			_UpperCAmelCase     :					str						)				->			Any:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      Any     =						self.get_parent_idx(_UpperCAmelCase						)
														while p >= 0 and self.heap[p] > self.heap[idx]:
																					SCREAMING_SNAKE_CASE__   ,SCREAMING_SNAKE_CASE__       :      Any     =						self.heap[idx], self.heap[p]
																					SCREAMING_SNAKE_CASE__   ,SCREAMING_SNAKE_CASE__       :      int     =						(
																					    self.idx_of_element[self.heap[idx]],
																					    self.idx_of_element[self.heap[p]],
																					)
																					SCREAMING_SNAKE_CASE__       :      Dict     =						p
																					SCREAMING_SNAKE_CASE__       :      List[str]     =						self.get_parent_idx(_UpperCAmelCase						)






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





														"""simple docstring"""
														return self.heap[0]






							def  A_     ( self     :					Tuple						)				->			List[Any]:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__   ,SCREAMING_SNAKE_CASE__       :      Optional[int]     =						self.heap[-1], self.heap[0]
														SCREAMING_SNAKE_CASE__   ,SCREAMING_SNAKE_CASE__       :      List[Any]     =						(
														    self.idx_of_element[self.heap[-1]],
														    self.idx_of_element[self.heap[0]],
														)

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






							def  A_     ( self     :					Union[str, Any],			_UpperCAmelCase     :					str						)				->			Optional[Any]:





														"""simple docstring"""
														self.heap.append(_UpperCAmelCase						)
														SCREAMING_SNAKE_CASE__       :      str     =						len(self.heap						) - 1
														SCREAMING_SNAKE_CASE__       :      Optional[Any]     =						node.val
														self.sift_up(len(self.heap						) - 1						)






							def  A_     ( self     :					Optional[int]						)				->			int:





														"""simple docstring"""
														return len(self.heap						) == 0






							def  A_     ( self     :					Any,			_UpperCAmelCase     :					Tuple,			_UpperCAmelCase     :					str						)				->			Dict:





														"""simple docstring"""
														assert (
														    self.heap[self.idx_of_element[node]].val > new_value
														), "newValue must be less that current value"
														SCREAMING_SNAKE_CASE__       :      Tuple     =						new_value
														SCREAMING_SNAKE_CASE__       :      List[Any]     =						new_value
														self.sift_up(self.idx_of_element[node]						)


_lowerCamelCase :    Tuple  							= Node('''R''', -1)
_lowerCamelCase :    int  							= Node('''B''', 6)
_lowerCamelCase :    str  							= Node('''A''', 3)
_lowerCamelCase :    Optional[Any]  							= Node('''X''', 1)
_lowerCamelCase :    str  							= Node('''E''', 4)

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

# Generating Min-Heap from array
_lowerCamelCase :    int  							= 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, -1_7)

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

if __name__ == "__main__":
		import doctest

		doctest.testmod()






