

class 	A_		(	SCREAMING_SNAKE_CASE    ):
							pass






class 	A_		(	SCREAMING_SNAKE_CASE    ):
							pass






class 	A_		:
							def __init__(		self		:      Optional[int]):
								__lowerCamelCase    :    List[str] 	=			[
								    [],
								    [],
								    [],
								]
							def    lowerCAmelCase					(		self		:      str       ,SCREAMING_SNAKE_CASE__		:      int       ,SCREAMING_SNAKE_CASE__		:      int):
								try:
									if len(self.queues[priority]) >= 1_0_0:
										raise OverflowError('Maximum queue size is 100')
									self.queues[priority].append(SCREAMING_SNAKE_CASE__)
								except IndexError:
									raise ValueError('Valid priorities are 0, 1, and 2')
							def    lowerCAmelCase					(		self		:      str):
								for queue in self.queues:
									if queue:
										return queue.pop(0)
								raise UnderFlowError('All queues are empty')


							def __str__(		self		:      List[str]):
								return "\n".join(F"Priority {i}: {q}" for i, q in enumerate(self.queues))






class 	A_		:
							def __init__(		self		:      List[str]):
								__lowerCamelCase    :    Any 	=			[]
							def    lowerCAmelCase					(		self		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      int):
								if len(self.queue) == 1_0_0:
									raise OverFlowError('Maximum queue size is 100')
								self.queue.append(SCREAMING_SNAKE_CASE__)
							def    lowerCAmelCase					(		self		:      Any):
								if not self.queue:
									raise UnderFlowError('The queue is empty')
								else:
									__lowerCamelCase    :    Optional[Any] 	=			min(self.queue)
									self.queue.remove(SCREAMING_SNAKE_CASE__)
									return data


							def __str__(		self		:      Any):
								return str(self.queue)






def        SCREAMING_SNAKE_CASE__	(  )  ->					Union[str, Any]:
	__lowerCamelCase    :    Dict 	=			FixedPriorityQueue()
	fpq.enqueue(0     ,			1_0      )
	fpq.enqueue(1     ,			7_0      )
	fpq.enqueue(0     ,			1_0_0      )
	fpq.enqueue(2     ,			1      )
	fpq.enqueue(2     ,			5      )
	fpq.enqueue(1     ,			7      )
	fpq.enqueue(2     ,			4      )
	fpq.enqueue(1     ,			6_4      )
	fpq.enqueue(0     ,			1_2_8      )
	print(lowerCamelCase__      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )
	print(lowerCamelCase__      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )
	print(fpq.dequeue()      )






def        SCREAMING_SNAKE_CASE__	(  )  ->					Optional[int]:
	__lowerCamelCase    :    Optional[int] 	=			ElementPriorityQueue()
	epq.enqueue(1_0      )
	epq.enqueue(7_0      )
	epq.enqueue(1_0_0      )
	epq.enqueue(1      )
	epq.enqueue(5      )
	epq.enqueue(7      )
	epq.enqueue(4      )
	epq.enqueue(6_4      )
	epq.enqueue(1_2_8      )
	print(lowerCamelCase__      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )
	print(lowerCamelCase__      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )
	print(epq.dequeue()      )


if __name__ == "__main__":
					fixed_priority_queue()
					element_priority_queue()







from __future__ import annotations






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)  ->					None:
	__lowerCamelCase    :    int 	=			len(lowerCamelCase__      )

	# If row is equal to the size of the board it means there are a queen in each row in
	# the current board (possible_board)
	if row == n:
		# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
		# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
		boards.append(['. ' * i + 'Q ' + '. ' * (n - 1 - i) for i in possible_board]      )
		return

	# We iterate each column in the row to find all possible results in each row
	for col in range(lowerCamelCase__      ):
		# We apply that we learned previously. First we check that in the current board
		# (possible_board) there are not other same value because if there is it means
		# that there are a collision in vertical. Then we apply the two formulas we
		# learned before:
		#
		# 45º: y - x = b or 45: row - col = b
		# 135º: y + x = b or row + col = b.
		#
		# And we verify if the results of this two formulas not exist in their variables
		# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
		#
		# If any or these are True it means there is a collision so we continue to the
		# next value in the for loop.
		if (
		    col in possible_board
		    or row - col in diagonal_right_collisions
		    or row + col in diagonal_left_collisions
		):
			continue

		# If it is False we call dfs function again and we update the inputs
		depth_first_search(
		    [*possible_board, col]     ,			[*diagonal_right_collisions, row - col]     ,			[*diagonal_left_collisions, row + col]     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					None:
	__lowerCamelCase    :    list[list[str]] 	=			[]
	depth_first_search([]     ,			[]     ,			[]     ,			lowerCamelCase__     ,			lowerCamelCase__      )

	# Print all the boards
	for board in boards:
		for column in board:
			print(lowerCamelCase__      )
		print(''      )

	print(len(lowerCamelCase__      )     ,			'solutions were found.'      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					n_queens_solution(4)




