


from __future__ import annotations

UpperCAmelCase__   	=							list[tuple[int, int]]

UpperCAmelCase__   	=							[
    [0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 1, 0, 0],
]

UpperCAmelCase__   	=							([-1, 0], [0, -1], [1, 0], [0, 1])  # up, left, down, right







class       lowerCamelCase__   :





     def __init__(self		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     )     ->   Dict:
      _lowercase							      =pos_x
      _lowercase							      =pos_y
      _lowercase							      =(pos_y, pos_x)
      _lowercase							      =goal_x
      _lowercase							      =goal_y
      _lowercase							      =g_cost
      _lowercase							      =parent
      _lowercase							      =self.calculate_heuristic()





     def      __A					(self       )     ->   float:
      _lowercase							      =abs(self.pos_x - self.goal_x       )
      _lowercase							      =abs(self.pos_y - self.goal_y       )
      return dx + dy





     def __lt__(self		,     UpperCAmelCase       )     ->   bool:
      return self.f_cost < other.f_cost







class       lowerCamelCase__   :





     def __init__(self		,     UpperCAmelCase		,     UpperCAmelCase       )     ->   List[Any]:
      _lowercase							      =Node(start[1]		,     start[0]		,     goal[1]		,     goal[0]		,     0		,     __lowerCAmelCase       )
      _lowercase							      =Node(goal[1]		,     goal[0]		,     goal[1]		,     goal[0]		,     9_9_9_9_9		,     __lowerCAmelCase       )

      _lowercase							      =[self.start]
      _lowercase							      =[]

      _lowercase							      =False





     def      __A					(self       )     ->   Path | None:






      while self.open_nodes:
       # Open Nodes are sorted using __lt__
       self.open_nodes.sort()
       _lowercase							      =self.open_nodes.pop(0       )

       if current_node.pos == self.target.pos:
        _lowercase							      =True
        return self.retrace_path(__lowerCAmelCase       )

       self.closed_nodes.append(__lowerCAmelCase       )
       _lowercase							      =self.get_successors(__lowerCAmelCase       )

       for child_node in successors:
        if child_node in self.closed_nodes:
         continue

        if child_node not in self.open_nodes:
         self.open_nodes.append(__lowerCAmelCase       )
        else:
         # retrieve the best current path
         _lowercase							      =self.open_nodes.pop(self.open_nodes.index(__lowerCAmelCase       )       )

         if child_node.g_cost < better_node.g_cost:
          self.open_nodes.append(__lowerCAmelCase       )
         else:
          self.open_nodes.append(__lowerCAmelCase       )

      if not self.reached:
       return [self.start.pos]
      return None





     def      __A					(self		,     UpperCAmelCase       )     ->   list[Node]:
      _lowercase							      =[]
      for action in delta:
       _lowercase							      =parent.pos_x + action[1]
       _lowercase							      =parent.pos_y + action[0]

       if not (0 <= pos_x <= len(grid[0]       ) - 1 and 0 <= pos_y <= len(__lowerCAmelCase       ) - 1):
        continue

       if grid[pos_y][pos_x] != 0:
        continue

       successors.append(
           Node(
               __lowerCAmelCase		,     __lowerCAmelCase		,     self.target.pos_y		,     self.target.pos_x		,     parent.g_cost + 1		,     __lowerCAmelCase		,     )       )
      return successors





     def      __A					(self		,     UpperCAmelCase       )     ->   Path:
      _lowercase							      =node
      _lowercase							      =[]
      while current_node is not None:
       path.append((current_node.pos_y, current_node.pos_x)       )
       _lowercase							      =current_node.parent
      path.reverse()
      return path


if __name__ == "__main__":
  UpperCAmelCase__   	=							(0, 0)
  UpperCAmelCase__   	=							(len(grid) - 1, len(grid[0]) - 1)
  for elem in grid:
    print(elem)

  print('''------''')

  UpperCAmelCase__   	=							GreedyBestFirst(init, goal)
  UpperCAmelCase__   	=							greedy_bf.search()
  if path:
    for pos_x, pos_y in path:
      UpperCAmelCase__   	=							2

    for elem in grid:
      print(elem)








from math import ceil







def    __lowerCamelCase					(							__a   :int = 1_0_0_1    )		->				int:






		"""simple docstring"""

		A__        =   1

		for i in range(1    ,     int(ceil(n / 2.0    )    )    ):
				A__        =   2 * i + 1
				A__        =   2 * i
				A__        =   total + 4 * odd**2 - 6 * even

		return total


if __name__ == "__main__":
					import sys

					if len(sys.argv) == 1:
										print(solution())
					else:
										try:
															A    :					List[str] =      int(sys.argv[1])
															print(solution(n))
										except ValueError:
															print('''Invalid entry - please enter a number''')



