





from __future__ import annotations

a__: Union[str, Any]							   =						list[tuple[int, int]]

a__: Dict							   =						[
    [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],
]

a__: Any							   =						([-1, 0], [0, -1], [1, 0], [0, 1])  # up, left, down, right




class        SCREAMING_SNAKE_CASE__					:



 def __init__(				self,__lowerCamelCase,__lowerCamelCase,__lowerCamelCase,__lowerCamelCase,__lowerCamelCase,__lowerCamelCase,):
        A__		   =		pos_x
        A__		   =		pos_y
        A__		   =		(pos_y, pos_x)
        A__		   =		goal_x
        A__		   =		goal_y
        A__		   =		g_cost
        A__		   =		parent
        A__		   =		self.calculate_heuristic()



 def 							UpperCamelCase     (				self					):
        A__		   =		abs(self.pos_x - self.goal_x					)
        A__		   =		abs(self.pos_y - self.goal_y					)
        return dx + dy




 def __lt__(				self,__lowerCamelCase					):
        return self.f_cost < other.f_cost




class        SCREAMING_SNAKE_CASE__					:



 def __init__(				self,__lowerCamelCase,__lowerCamelCase					):
        A__		   =		Node(start[1],start[0],goal[1],goal[0],0,__lowerCamelCase					)
        A__		   =		Node(goal[1],goal[0],goal[1],goal[0],9_9999,__lowerCamelCase					)

        A__		   =		[self.start]
        A__		   =		[]

        A__		   =		False



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

               if current_node.pos == self.target.pos:
                      A__		   =		True
                      return self.retrace_path(__lowerCamelCase					)

               self.closed_nodes.append(__lowerCamelCase					)
               A__		   =		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
                             A__		   =		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 							UpperCamelCase     (				self,__lowerCamelCase					):
        A__		   =		[]
        for action in delta:
               A__		   =		parent.pos_x + action[1]
               A__		   =		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 							UpperCamelCase     (				self,__lowerCamelCase					):
        A__		   =		node
        A__		   =		[]
        while current_node is not None:
               path.append((current_node.pos_y, current_node.pos_x)					)
               A__		   =		current_node.parent
        path.reverse()
        return path


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

       print('------')

       a__: int							   =						GreedyBestFirst(init, goal)
       a__: List[Any]							   =						greedy_bf.search()
       if path:
              for pos_x, pos_y in path:
                     a__: int							   =						2

              for elem in grid:
                     print(elem)












import itertools
import math


def       UpperCamelCase__(			UpperCamelCase__     :			int    )->bool:

       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5					,	int(math.sqrt(UpperCamelCase__    ) + 1    )					,	6    ):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True


def       UpperCamelCase__(			)->Tuple:
       A__		   =		2
       while True:
              if is_prime(UpperCamelCase__    ):
                     yield num
              num += 1


def       UpperCamelCase__(			UpperCamelCase__     :			int = 1_00_01    )->int:
       return next(itertools.islice(prime_generator()					,	nth - 1					,	UpperCamelCase__    )    )


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





