


class   _lowerCamelCase :




       """simple docstring"""



       def __init__(      self				,       _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)->Optional[int]:




         '''simple docstring'''





         A_      :				int		     =					name
         A_      :				Any		     =					val



       def __str__(      self		)->Optional[Any]:




         '''simple docstring'''





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







       def __lt__(      self				,       _SCREAMING_SNAKE_CASE		)->List[Any]:




         '''simple docstring'''





         return self.val < other.val






class   _lowerCamelCase :




       """simple docstring"""



       def __init__(      self				,       _SCREAMING_SNAKE_CASE		)->Optional[Any]:




         '''simple docstring'''





         A_      :				Union[str, Any]		     =					{}
         A_      :				int		     =					{}
         A_      :				List[Any]		     =					self.build_heap(_SCREAMING_SNAKE_CASE		)



       def __getitem__(      self				,       _SCREAMING_SNAKE_CASE		)->int:




         '''simple docstring'''





         return self.get_value(_SCREAMING_SNAKE_CASE		)



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->int:




         '''simple docstring'''





         return (idx - 1) // 2



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->str:




         '''simple docstring'''





         return idx * 2 + 1



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->Any:




         '''simple docstring'''





         return idx * 2 + 2



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->Dict:




         '''simple docstring'''





         return self.heap_dict[key]



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->Optional[int]:




         '''simple docstring'''





         A_      :				List[str]		     =					len(_SCREAMING_SNAKE_CASE		) - 1
         A_      :				List[Any]		     =					self.get_parent_idx(_SCREAMING_SNAKE_CASE		)

         for idx, i in enumerate(_SCREAMING_SNAKE_CASE		):
           A_      :				Dict		     =					idx
           A_      :				Dict		     =					i.val

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



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)->str:




         '''simple docstring'''





         while True:
           A_      :				str		     =					self.get_left_child_idx(_SCREAMING_SNAKE_CASE		)  # noqa: E741
           A_      :				Dict		     =					self.get_right_child_idx(_SCREAMING_SNAKE_CASE		)

           A_      :				Optional[Any]		     =					idx
           if l < len(_SCREAMING_SNAKE_CASE		) and array[l] < array[idx]:
             A_      :				Optional[Any]		     =					l
           if r < len(_SCREAMING_SNAKE_CASE		) and array[r] < array[smallest]:
             A_      :				Tuple		     =					r

           if smallest != idx:
             A_     ,       A_      :				Tuple		     =					array[smallest], array[idx]
             (
                 (
                 A_
             )     ,       (
                 A_
             )     ,       
             )      :				Union[str, Any]		     =					(
                 self.idx_of_element[array[smallest]],
                 self.idx_of_element[array[idx]],
             )
             A_      :				Optional[int]		     =					smallest
           else:
             break



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->Any:




         '''simple docstring'''





         A_      :				List[Any]		     =					self.get_parent_idx(_SCREAMING_SNAKE_CASE		)
         while p >= 0 and self.heap[p] > self.heap[idx]:
           A_     ,       A_      :				Union[str, Any]		     =					self.heap[idx], self.heap[p]
           A_     ,       A_      :				int		     =					(
               self.idx_of_element[self.heap[idx]],
               self.idx_of_element[self.heap[p]],
           )
           A_      :				Optional[int]		     =					p
           A_      :				int		     =					self.get_parent_idx(_SCREAMING_SNAKE_CASE		)



       def        _snake_case       (      self		)->str:




         '''simple docstring'''





         return self.heap[0]



       def        _snake_case       (      self		)->Tuple:




         '''simple docstring'''





         A_     ,       A_      :				Union[str, Any]		     =					self.heap[-1], self.heap[0]
         A_     ,       A_      :				Union[str, Any]		     =					(
             self.idx_of_element[self.heap[-1]],
             self.idx_of_element[self.heap[0]],
         )

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



       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->Any:




         '''simple docstring'''





         self.heap.append(_SCREAMING_SNAKE_CASE		)
         A_      :				int		     =					len(self.heap		) - 1
         A_      :				Optional[Any]		     =					node.val
         self.sift_up(len(self.heap		) - 1		)



       def        _snake_case       (      self		)->List[Any]:




         '''simple docstring'''





         return len(self.heap		) == 0







       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)->List[Any]:




         '''simple docstring'''





         assert (
             self.heap[self.idx_of_element[node]].val > new_value
         ), "newValue must be less that current value"
         A_      :				Optional[int]		     =					new_value
         A_      :				Union[str, Any]		     =					new_value
         self.sift_up(self.idx_of_element[node]		)




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

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

# Generating Min-Heap from array
UpperCamelCase								=	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()








def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE       ):
  A_      :				List[Any]		     =					current_set.copy()
  for row_index, row in enumerate(SCREAMING_SNAKE_CASE       ):
    A_      :				List[str]		     =					row[0]
    for column_index, column in enumerate(SCREAMING_SNAKE_CASE       ):
      if magnitude == 0:
        A_      :				Union[str, Any]		     =					column
        continue
      A_      :				Dict		     =					column / magnitude
    # Subtract to cancel term
  A_      :				Union[str, Any]		     =					current_set[0]
  A_      :				Tuple		     =					[first_row]
  A_      :				int		     =					current_set[1::]
  for row in current_set:
    A_      :				Tuple		     =					[]
    # If first term is 0, it is already in form we want, so we preserve it
    if row[0] == 0:
      final_set.append(SCREAMING_SNAKE_CASE       )
      continue
    for column_index in range(len(SCREAMING_SNAKE_CASE       )       ):
      temp_row.append(first_row[column_index] - row[column_index]       )
    final_set.append(SCREAMING_SNAKE_CASE       )
  # Create next recursion iteration set
  if len(final_set[0]       ) != 3:
    A_      :				Optional[Any]		     =					final_set[0]
    A_      :				Any		     =					[]
    A_      :				str		     =					[]
    for row in final_set[1::]:
      current_first_column.append(row[0]       )
      next_iteration.append(row[1::]       )
    A_      :				Optional[Any]		     =					simplify(SCREAMING_SNAKE_CASE       )
    for i in range(len(SCREAMING_SNAKE_CASE       )       ):
      resultant[i].insert(0 ,			current_first_column[i]       )
    resultant.insert(0 ,			SCREAMING_SNAKE_CASE       )
    A_      :				List[Any]		     =					resultant
  return final_set


def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE       ):
  if len(SCREAMING_SNAKE_CASE       ) == 0:
    raise IndexError('''solve_simultaneous() requires n lists of length n+1'''       )
  A_      :				str		     =					len(SCREAMING_SNAKE_CASE       ) + 1
  if any(len(SCREAMING_SNAKE_CASE       ) != _length for item in equations       ):
    raise IndexError('''solve_simultaneous() requires n lists of length n+1'''       )
  for row in equations:
    if any(not isinstance(SCREAMING_SNAKE_CASE ,			(int, float)       ) for column in row       ):
      raise ValueError('''solve_simultaneous() requires lists of integers'''       )
  if len(SCREAMING_SNAKE_CASE       ) == 1:
    return [equations[0][-1] / equations[0][0]]
  A_      :				Dict		     =					equations.copy()
  if any(0 in row for row in data_set       ):
    A_      :				Tuple		     =					data_set.copy()
    A_      :				Optional[Any]		     =					[]
    for row_index, row in enumerate(SCREAMING_SNAKE_CASE       ):
      if 0 not in row:
        A_      :				str		     =					data_set.pop(SCREAMING_SNAKE_CASE       )
        break
    if not full_row:
      raise ValueError('''solve_simultaneous() requires at least 1 full equation'''       )
    data_set.insert(0 ,			SCREAMING_SNAKE_CASE       )
  A_      :				int		     =					data_set.copy()
  A_      :				Dict		     =					simplify(SCREAMING_SNAKE_CASE       )
  A_      :				Dict		     =					simplified[::-1]
  A_      :				list		     =					[]
  for row in simplified:
    A_      :				Union[str, Any]		     =					row[-1]
    if not solutions:
      if row[-2] == 0:
        solutions.append(0       )
        continue
      solutions.append(current_solution / row[-2]       )
      continue
    A_      :				Optional[Any]		     =					row.copy()[: len(SCREAMING_SNAKE_CASE       ) - 1 :]
    while temp_row[0] == 0:
      temp_row.pop(0       )
    if len(SCREAMING_SNAKE_CASE       ) == 0:
      solutions.append(0       )
      continue
    A_      :				int		     =					temp_row[1::]
    A_      :				int		     =					temp_row[::-1]
    for column_index, column in enumerate(SCREAMING_SNAKE_CASE       ):
      current_solution -= column * solutions[column_index]
    solutions.append(SCREAMING_SNAKE_CASE       )
  A_      :				Union[str, Any]		     =					[]
  for item in solutions:
    final.append(float(round(SCREAMING_SNAKE_CASE ,			5       )       )       )
  return final[::-1]


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     UpperCamelCase								=	[
         [2, 1, 1, 1, 1, 4],
         [1, 2, 1, 1, 1, 5],
         [1, 1, 2, 1, 1, 6],
         [1, 1, 1, 2, 1, 7],
         [1, 1, 1, 1, 2, 8],
     ]
     print(solve_simultaneous(eq))
     print(solve_simultaneous([[4, 2]]))




