






"""simple docstring"""
from __future__ import annotations

import time

lowerCamelCase_       			=   list[tuple[int, int]]

lowerCamelCase_       			=   [
    [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],
]

lowerCamelCase_       			=   [[-1, 0], [0, -1], [1, 0], [0, 1]]  # up, left, down, right







class     UpperCamelCase_ :





	def __init__(   self      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				Node | None		)		->    List[str]:
				UpperCAmelCase_  :				List[Any]      =      pos_x
				UpperCAmelCase_  :				Dict      =      pos_y
				UpperCAmelCase_  :				List[Any]      =      (pos_y, pos_x)
				UpperCAmelCase_  :				int      =      goal_x
				UpperCAmelCase_  :				int      =      goal_y
				UpperCAmelCase_  :				Union[str, Any]      =      parent







class     UpperCamelCase_ :





	def __init__(   self      :				Dict			,			lowerCAmelCase_      :				tuple[int, int]			,			lowerCAmelCase_      :				tuple[int, int]		)		->    int:
				UpperCAmelCase_  :				Dict      =      Node(start[1]			,			start[0]			,			goal[1]			,			goal[0]			,			lowerCAmelCase_		)
				UpperCAmelCase_  :				List[str]      =      Node(goal[1]			,			goal[0]			,			goal[1]			,			goal[0]			,			lowerCAmelCase_		)

				UpperCAmelCase_  :				List[str]      =      [self.start]
				UpperCAmelCase_  :				List[Any]      =      False





	def   _SCREAMING_SNAKE_CASE   (   self      :				int		)		->    Path | None:
				while self.node_queue:
							UpperCAmelCase_  :				Optional[int]      =      self.node_queue.pop(0		)

							if current_node.pos == self.target.pos:
										UpperCAmelCase_  :				int      =      True
										return self.retrace_path(lowerCAmelCase_		)

							UpperCAmelCase_  :				Union[str, Any]      =      self.get_successors(lowerCAmelCase_		)

							for node in successors:
										self.node_queue.append(lowerCAmelCase_		)

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





	def   _SCREAMING_SNAKE_CASE   (   self      :				Tuple			,			lowerCAmelCase_      :				Node		)		->    list[Node]:
				UpperCAmelCase_  :				Union[str, Any]      =      []
				for action in delta:
							UpperCAmelCase_  :				Optional[Any]      =      parent.pos_x + action[1]
							UpperCAmelCase_  :				Tuple      =      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			,			lowerCAmelCase_		)		)
				return successors





	def   _SCREAMING_SNAKE_CASE   (   self      :				Union[str, Any]			,			lowerCAmelCase_      :				Node | None		)		->    Path:
				UpperCAmelCase_  :				Any      =      node
				UpperCAmelCase_  :				Any      =      []
				while current_node is not None:
							path.append((current_node.pos_y, current_node.pos_x)		)
							UpperCAmelCase_  :				int      =      current_node.parent
				path.reverse()
				return path







class     UpperCamelCase_ :





	def __init__(   self      :				str			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				Tuple		)		->    Tuple:
				UpperCAmelCase_  :				Union[str, Any]      =      BreadthFirstSearch(lowerCAmelCase_			,			lowerCAmelCase_		)
				UpperCAmelCase_  :				Any      =      BreadthFirstSearch(lowerCAmelCase_			,			lowerCAmelCase_		)
				UpperCAmelCase_  :				Any      =      False





	def   _SCREAMING_SNAKE_CASE   (   self      :				List[Any]		)		->    Path | None:
				while self.fwd_bfs.node_queue or self.bwd_bfs.node_queue:
							UpperCAmelCase_  :				List[Any]      =      self.fwd_bfs.node_queue.pop(0		)
							UpperCAmelCase_  :				Tuple      =      self.bwd_bfs.node_queue.pop(0		)

							if current_bwd_node.pos == current_fwd_node.pos:
										UpperCAmelCase_  :				Optional[int]      =      True
										return self.retrace_bidirectional_path(
										    lowerCAmelCase_			,			lowerCAmelCase_		)

							UpperCAmelCase_  :				Any      =      current_bwd_node
							UpperCAmelCase_  :				Optional[int]      =      current_fwd_node

							UpperCAmelCase_  :				Any      =      {
							    self.fwd_bfs: self.fwd_bfs.get_successors(lowerCAmelCase_		),
							    self.bwd_bfs: self.bwd_bfs.get_successors(lowerCAmelCase_		),
							}

							for bfs in [self.fwd_bfs, self.bwd_bfs]:
										for node in successors[bfs]:
													bfs.node_queue.append(lowerCAmelCase_		)

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





	def   _SCREAMING_SNAKE_CASE   (   self      :				int			,			lowerCAmelCase_      :				Node			,			lowerCAmelCase_      :				Node		)		->    Path:
				UpperCAmelCase_  :				Tuple      =      self.fwd_bfs.retrace_path(lowerCAmelCase_		)
				UpperCAmelCase_  :				str      =      self.bwd_bfs.retrace_path(lowerCAmelCase_		)
				bwd_path.pop()
				bwd_path.reverse()
				UpperCAmelCase_  :				int      =      fwd_path + bwd_path
				return path


if __name__ == "__main__":
			# all coordinates are given in format [y,x]
			import doctest

			doctest.testmod()
			lowerCamelCase_       			=   (0, 0)
			lowerCamelCase_       			=   (len(grid) - 1, len(grid[0]) - 1)
			for elem in grid:
						print(elem)

			lowerCamelCase_       			=   time.time()
			lowerCamelCase_       			=   BreadthFirstSearch(init, goal)
			lowerCamelCase_       			=   bfs.search()
			lowerCamelCase_       			=   time.time() - start_bfs_time

			print('''Unidirectional BFS computation time : ''', bfs_time)

			lowerCamelCase_       			=   time.time()
			lowerCamelCase_       			=   BidirectionalBreadthFirstSearch(init, goal)
			lowerCamelCase_       			=   bd_bfs.search()
			lowerCamelCase_       			=   time.time() - start_bd_bfs_time

			print('''Bidirectional BFS computation time : ''', bd_bfs_time)











"""simple docstring"""
from __future__ import annotations

import math

def        snake_case   (     A__		):

			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(A__		) + 1		)			,6		):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True


lowerCamelCase_       			=   [num for num in range(3, 10_0001, 2) if not is_prime(num)]

def        snake_case   (     A__		):
			if not isinstance(A__			,A__		):
						raise ValueError("n must be an integer"		)
			if n <= 0:
						raise ValueError("n must be >= 0"		)

			UpperCAmelCase_  :				List[str]      =      []
			for num in range(len(A__		)		):
						UpperCAmelCase_  :				Dict      =      0
						while 2 * i * i <= odd_composites[num]:
									UpperCAmelCase_  :				List[str]      =      odd_composites[num] - 2 * i * i
									if is_prime(A__		):
												break
									i += 1
						else:
									list_nums.append(odd_composites[num]		)
									if len(A__		) == n:
												return list_nums

			return []

def        snake_case   (     ):
			return compute_nums(1		)[0]


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



