




'''simple docstring'''






from collections import OrderedDict
from typing import Any, Mapping, Optional

from ... import PreTrainedTokenizer, TensorType, is_torch_available
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfigWithPast
from ...utils import logging


_lowerCAmelCase      	=					logging.get_logger(__name__)

_lowerCAmelCase      	=					{
    '''EleutherAI/gpt-neo-1.3B''': '''https://huggingface.co/EleutherAI/gpt-neo-1.3B/resolve/main/config.json''',
    # See all GPTNeo models at https://huggingface.co/models?filter=gpt_neo
}



class 					A		( __lowerCamelCase		):




				'''simple docstring'''





				A      	=				'gpt_neo'
				A      	=				['past_key_values']
				A      	=				{'num_attention_heads': 'num_heads', 'num_hidden_layers': 'num_layers'}
				def __init__(self ,  _UpperCAmelCase=5_0_2_5_7 ,  _UpperCAmelCase=2_0_4_8 ,  _UpperCAmelCase=2_0_4_8 ,  _UpperCAmelCase=2_4 ,  _UpperCAmelCase=[[["global", "local"], 1_2]] ,  _UpperCAmelCase=1_6 ,  _UpperCAmelCase=None ,  _UpperCAmelCase=2_5_6 ,  _UpperCAmelCase="gelu_new" ,  _UpperCAmelCase=0.0 ,  _UpperCAmelCase=0.0 ,  _UpperCAmelCase=0.0 ,  _UpperCAmelCase=0.1 ,  _UpperCAmelCase=1E-5 ,  _UpperCAmelCase=0.02 ,  _UpperCAmelCase=True ,  _UpperCAmelCase=5_0_2_5_6 ,  _UpperCAmelCase=5_0_2_5_6 ,  **_UpperCAmelCase ,  )	->       Tuple:
							__UpperCamelCase      :			Tuple									=   vocab_size
							__UpperCamelCase      :			Union[str, Any]									=   max_position_embeddings
							__UpperCamelCase      :			List[Any]									=   hidden_size
							__UpperCamelCase      :			str									=   num_layers
							__UpperCamelCase      :			Any									=   num_heads
							__UpperCamelCase      :			List[str]									=   intermediate_size
							__UpperCamelCase      :			Optional[Any]									=   window_size
							__UpperCamelCase      :			int									=   activation_function
							__UpperCamelCase      :			List[Any]									=   resid_dropout
							__UpperCamelCase      :			Union[str, Any]									=   embed_dropout
							__UpperCamelCase      :			int									=   attention_dropout
							__UpperCamelCase      :			Optional[int]									=   classifier_dropout
							__UpperCamelCase      :			Dict									=   layer_norm_epsilon
							__UpperCamelCase      :			Tuple									=   initializer_range
							__UpperCamelCase      :			Dict									=   use_cache

							__UpperCamelCase      :			Union[str, Any]									=   bos_token_id
							__UpperCamelCase      :			Any									=   eos_token_id

							__UpperCamelCase      :			Dict									=   attention_types
							__UpperCamelCase      :			str									=   self.expand_attention_types_params(UpperCamelCase_			)

							if len(self.attention_layers			) != self.num_layers:
										raise ValueError(
										    "Configuration for convolutional module is incorrect. "
										    "It is required that `len(config.attention_layers)` == `config.num_layers` "
										    f"but is `len(config.attention_layers) = {len(self.attention_layers			)}`, "
										    f"`config.num_layers = {self.num_layers}`. "
										    "`config.attention_layers` is prepared using `config.attention_types`. "
										    "Please verify the value of `config.attention_types` argument."			)

							super().__init__(bos_token_id=UpperCamelCase_ ,  eos_token_id=UpperCamelCase_ ,  **UpperCamelCase_			)





				@staticmethod
				def        a_       (_UpperCAmelCase			)	->       Union[str, Any]:
							__UpperCamelCase      :			Optional[int]									=   []
							for item in attention_types:
										for _ in range(item[1]			):
													attentions.extend(item[0]			)
							return attentions







def 			__lowerCAmelCase					(    snake_case__					,      snake_case__					,      snake_case__					,      snake_case__						):
			import torch

			__UpperCamelCase      :			str									=   input.size()
			__UpperCamelCase      :			List[Any]									=   len(A__						)
			__UpperCamelCase      :			Tuple									=   shape[dimension]

			__UpperCamelCase      :			str									=   torch.arange(0					,      A__					,      A__						)
			__UpperCamelCase      :			Tuple									=   torch.div(sizedim - size					,      A__					,      rounding_mode="floor"						) + 1
			__UpperCamelCase      :			List[str]									=   torch.arange(A__						) + low_indices[:min_length][:, None]

			__UpperCamelCase      :			str									=   [slice(A__						)] * rank
			__UpperCamelCase      :			int									=   indices
			__UpperCamelCase      :			Dict									=   input[s]

			__UpperCamelCase      :			List[str]									=   list(range(0					,      rank + 1						)						)
			perm.append(perm.pop(dimension + 1						)						)

			return sliced.permute(A__						)

def 			__lowerCAmelCase					(    snake_case__					,      snake_case__						):
			import torch

			__UpperCamelCase      :			Union[str, Any]									=   torch.arange(1					,      A__						)
			__UpperCamelCase      :			int									=   torch.remainder(A__					,      A__						)
			__UpperCamelCase      :			Optional[Any]									=   remainders == 0
			__UpperCamelCase      :			str									=   candidates[divisor_indices]
			__UpperCamelCase      :			Dict									=   torch.max(A__						)
			return largest_divisor, torch.div(A__					,      A__					,      rounding_mode="floor"						)




class 					A		( __lowerCamelCase		):




				'''simple docstring'''





				@property
				def        a_       (self			)	->       Union[str, Any]:
							__UpperCamelCase      :			int									=   OrderedDict({"input_ids": {0: "batch", 1: "sequence"}}			)
							if self.use_past:
										self.fill_with_past_key_values_(UpperCamelCase_ ,  direction="inputs"			)
										__UpperCamelCase      :			Tuple									=   {0: "batch", 1: "past_sequence + sequence"}
							else:
										__UpperCamelCase      :			Union[str, Any]									=   {0: "batch", 1: "sequence"}

							return common_inputs
				@property
				def        a_       (self			)	->       List[str]:
							return self._config.num_heads
				def        a_       (self ,  _UpperCAmelCase ,  _UpperCAmelCase = -1 ,  _UpperCAmelCase = -1 ,  _UpperCAmelCase = False ,  _UpperCAmelCase = None ,  )	->       int:
							__UpperCamelCase      :			Tuple									=   super(UpperCamelCase_ ,  self			).generate_dummy_inputs(
							    UpperCamelCase_ ,  batch_size=UpperCamelCase_ ,  seq_length=UpperCamelCase_ ,  is_pair=UpperCamelCase_ ,  framework=UpperCamelCase_			)

							# We need to order the input in the way they appears in the forward()
							__UpperCamelCase      :			Any									=   OrderedDict({"input_ids": common_inputs["input_ids"]}			)

							# Need to add the past_keys
							if self.use_past:
										if not is_torch_available():
													raise ValueError("Cannot generate dummy past_keys inputs without PyTorch installed."			)
										else:
													import torch

													__UpperCamelCase		,					__UpperCamelCase      :			Any									=   common_inputs["input_ids"].shape
													# Not using the same length for past_key_values
													__UpperCamelCase      :			Optional[Any]									=   seqlen + 2
													__UpperCamelCase      :			Any									=   (
													    batch,
													    self.num_attention_heads,
													    past_key_values_length,
													    self._config.hidden_size // self.num_attention_heads,
													)
													__UpperCamelCase      :			Any									=   [
													    (torch.zeros(UpperCamelCase_			), torch.zeros(UpperCamelCase_			)) for _ in range(self.num_layers			)
													]

							__UpperCamelCase      :			Optional[int]									=   common_inputs["attention_mask"]
							if self.use_past:
										__UpperCamelCase      :			Dict									=   ordered_inputs["attention_mask"].dtype
										__UpperCamelCase      :			int									=   torch.cat(
										    [ordered_inputs["attention_mask"], torch.ones(UpperCamelCase_ ,  UpperCamelCase_ ,  dtype=UpperCamelCase_			)] ,  dim=1			)

							return ordered_inputs





				@property
				def        a_       (self			)	->       List[Any]:
							return 1_3









from __future__ import annotations




def 					lowerCamelCase__       (						A__       :					list[int]  ,			A__       :					list[int]  ,			A__       :					list[int]  ,			A__       :					list[list[str]]  ,			A__       :					int  ,			):





       '''simple docstring'''



       __lowerCamelCase   =						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 					lowerCamelCase__       (						A__       :					int	):





       '''simple docstring'''



       __lowerCamelCase   =						[]
       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)

