


'''simple docstring'''
from __future__ import annotations







def       a_				(	UpperCamelCase_						,  UpperCamelCase_						,  UpperCamelCase_						,  UpperCamelCase_						,  UpperCamelCase_						,  ):
							A_			    =		len(UpperCAmelCase_ )

							# 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(UpperCAmelCase_ ):
														# 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]						,  UpperCAmelCase_						,  UpperCAmelCase_						,  )







def       a_				(	UpperCamelCase_ ):
							A_			    =		[]
							depth_first_search([]						,  []						,  []						,  UpperCAmelCase_						,  UpperCAmelCase_ )

							# Print all the boards
							for board in boards:
														for column in board:
																					print(UpperCAmelCase_ )
														print("" )

							print(len(UpperCAmelCase_ )						,  "solutions were found." )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							n_queens_solution(4)









'''simple docstring'''



from typing import TYPE_CHECKING

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


if is_sentencepiece_available():
      from ..ta.tokenization_ta import TaTokenizer
else:
      from ...utils.dummy_sentencepiece_objects import TaTokenizer

A__						:   int				=    TaTokenizer

if is_tokenizers_available():
      from ..ta.tokenization_ta_fast import TaTokenizerFast
else:
      from ...utils.dummy_tokenizers_objects import TaTokenizerFast

A__						:   Dict				=    TaTokenizerFast

A__						:   Dict				=    {"""configuration_mt5""": ["""MT5Config""", """MT5OnnxConfig"""]}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A__						:   Any				=    [
          """MT5EncoderModel""",
          """MT5ForConditionalGeneration""",
          """MT5ForQuestionAnswering""",
          """MT5Model""",
          """MT5PreTrainedModel""",
          """MT5Stack""",
      ]

try:
      if not is_tf_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A__						:   str				=    ["""TFMT5EncoderModel""", """TFMT5ForConditionalGeneration""", """TFMT5Model"""]

try:
      if not is_flax_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A__						:   str				=    ["""FlaxMT5EncoderModel""", """FlaxMT5ForConditionalGeneration""", """FlaxMT5Model"""]


if TYPE_CHECKING:
      from .configuration_mta import MTaConfig, MTaOnnxConfig

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_mta import (
                MTaEncoderModel,
                MTaForConditionalGeneration,
                MTaForQuestionAnswering,
                MTaModel,
                MTaPreTrainedModel,
                MTaStack,
            )

      try:
            if not is_tf_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tf_mta import TFMTaEncoderModel, TFMTaForConditionalGeneration, TFMTaModel

      try:
            if not is_flax_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_flax_mta import FlaxMTaEncoderModel, FlaxMTaForConditionalGeneration, FlaxMTaModel

else:
      import sys

      A__						:   Union[str, Any]				=    _LazyModule(
          __name__,
          globals()["""__file__"""],
          _import_structure,
          extra_objects={"""MT5Tokenizer""": MTaTokenizer, """MT5TokenizerFast""": MTaTokenizerFast},
          module_spec=__spec__,
      )






