






from __future__ import annotations







def       lowercase__	(					A_:						List[Any]  ,      A_:						int  ,      A_:						Dict  ,      A_:						int  ,      A_:						List[Any]  ,      )	->				None:







       """simple docstring"""






       __UpperCAmelCase     				=len(A_		)

       # 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(A_		):
              # 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]  ,      A_  ,      A_  ,      )







def       lowercase__	(					A_:						Optional[Any]		)	->				None:







       """simple docstring"""






       __UpperCAmelCase     				=[]
       depth_first_search([]  ,      []  ,      []  ,      A_  ,      A_		)

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

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   n_queens_solution(4)








'''simple docstring'''






from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch
import torch.nn as nn

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, apply_forward_hook
from .modeling_utils import ModelMixin
from .vae import Decoder, DecoderOutput, Encoder, VectorQuantizer




@dataclass
class 						a__							(				a__    ):





							'''simple docstring'''






							lowercase__     :  torch.FloatTensor




class 						a__							(				a__							,							a__    ):





							'''simple docstring'''






							@register_to_config
							def __init__(						self   ,       lowerCamelCase_ = 3   ,       lowerCamelCase_ = 3   ,       lowerCamelCase_ = ("DownEncoderBlock2D",)   ,       lowerCamelCase_ = ("UpDecoderBlock2D",)   ,       lowerCamelCase_ = (64,)   ,       lowerCamelCase_ = 1   ,       lowerCamelCase_ = "silu"   ,       lowerCamelCase_ = 3   ,       lowerCamelCase_ = 32   ,       lowerCamelCase_ = 2_56   ,       lowerCamelCase_ = 32   ,       lowerCamelCase_ = None   ,       lowerCamelCase_ = 0.18_215   ,       lowerCamelCase_ = "group"   ,       )			->				Union[str, Any]:
														super().__init__()

														# pass init params to Encoder
														lowerCAmelCase__			  =      Encoder(
														    in_channels=lowerCamelCase_   ,       out_channels=lowerCamelCase_   ,       down_block_types=lowerCamelCase_   ,       block_out_channels=lowerCamelCase_   ,       layers_per_block=lowerCamelCase_   ,       act_fn=lowerCamelCase_   ,       norm_num_groups=lowerCamelCase_   ,       double_z=lowerCamelCase_   ,       )

														lowerCAmelCase__			  =      vq_embed_dim if vq_embed_dim is not None else latent_channels

														lowerCAmelCase__			  =      nn.Convad(lowerCamelCase_   ,       lowerCamelCase_   ,       1  )
														lowerCAmelCase__			  =      VectorQuantizer(lowerCamelCase_   ,       lowerCamelCase_   ,       beta=0.25   ,       remap=lowerCamelCase_   ,       sane_index_shape=lowerCamelCase_  )
														lowerCAmelCase__			  =      nn.Convad(lowerCamelCase_   ,       lowerCamelCase_   ,       1  )

														# pass init params to Decoder
														lowerCAmelCase__			  =      Decoder(
														    in_channels=lowerCamelCase_   ,       out_channels=lowerCamelCase_   ,       up_block_types=lowerCamelCase_   ,       block_out_channels=lowerCamelCase_   ,       layers_per_block=lowerCamelCase_   ,       act_fn=lowerCamelCase_   ,       norm_num_groups=lowerCamelCase_   ,       norm_type=lowerCamelCase_   ,       )







							@apply_forward_hook
							def     __SCREAMING_SNAKE_CASE				(						self   ,       lowerCamelCase_   ,       lowerCamelCase_ = True  )			->				VQEncoderOutput:
														lowerCAmelCase__			  =      self.encoder(lowerCamelCase_  )
														lowerCAmelCase__			  =      self.quant_conv(lowerCamelCase_  )

														if not return_dict:
																					return (h,)

														return VQEncoderOutput(latents=lowerCamelCase_  )







							@apply_forward_hook
							def     __SCREAMING_SNAKE_CASE				(						self   ,       lowerCamelCase_   ,       lowerCamelCase_ = False   ,       lowerCamelCase_ = True  )			->				Union[DecoderOutput, torch.FloatTensor]:
														# also go through quantization layer
														if not force_not_quantize:
																					lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__			  =      self.quantize(lowerCamelCase_  )
														else:
																					lowerCAmelCase__			  =      h
														lowerCAmelCase__			  =      self.post_quant_conv(lowerCamelCase_  )
														lowerCAmelCase__			  =      self.decoder(lowerCamelCase_   ,       quant if self.config.norm_type == '''spatial''' else None  )

														if not return_dict:
																					return (dec,)

														return DecoderOutput(sample=lowerCamelCase_  )







							def     __SCREAMING_SNAKE_CASE				(						self   ,       lowerCamelCase_   ,       lowerCamelCase_ = True  )			->				Union[DecoderOutput, torch.FloatTensor]:
														lowerCAmelCase__			  =      sample
														lowerCAmelCase__			  =      self.encode(lowerCamelCase_  ).latents
														lowerCAmelCase__			  =      self.decode(lowerCamelCase_  ).sample

														if not return_dict:
																					return (dec,)

														return DecoderOutput(sample=lowerCamelCase_  )