


from __future__ import annotations



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   )-> None:
				lowerCAmelCase_ :      Dict    				=				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 			lowerCAmelCase (		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)



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


_UpperCAmelCase			:  Union[str, Any]     ={
    """configuration_llama""": ["""LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP""", """LlamaConfig"""],
}

try:
						if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_UpperCAmelCase			:  Optional[Any]     =["""LlamaTokenizer"""]

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_UpperCAmelCase			:  Optional[int]     =["""LlamaTokenizerFast"""]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_UpperCAmelCase			:  Tuple     =[
						    """LlamaForCausalLM""",
						    """LlamaModel""",
						    """LlamaPreTrainedModel""",
						    """LlamaForSequenceClassification""",
						]


if TYPE_CHECKING:
						from .configuration_llama import LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP, LlamaConfig

						try:
												if not is_sentencepiece_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_llama import LlamaTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_llama_fast import LlamaTokenizerFast

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_llama import LlamaForCausalLM, LlamaForSequenceClassification, LlamaModel, LlamaPreTrainedModel


else:
						import sys

						_UpperCAmelCase			:  List[Any]     =_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)