




def    UpperCAmelCase_				( __UpperCAmelCase		:      list[list]				)   ->					list[list]:
      SCREAMING_SNAKE_CASE_      		=     current_set.copy()
      for row_index, row in enumerate(__UpperCAmelCase				):
            SCREAMING_SNAKE_CASE_      		=     row[0]
            for column_index, column in enumerate(__UpperCAmelCase				):
                  if magnitude == 0:
                        SCREAMING_SNAKE_CASE_      		=     column
                        continue
                  SCREAMING_SNAKE_CASE_      		=     column / magnitude
    # Subtract to cancel term
      SCREAMING_SNAKE_CASE_      		=     current_set[0]
      SCREAMING_SNAKE_CASE_      		=     [first_row]
      SCREAMING_SNAKE_CASE_      		=     current_set[1::]
      for row in current_set:
            SCREAMING_SNAKE_CASE_      		=     []
            # If first term is 0, it is already in form we want, so we preserve it
            if row[0] == 0:
                  final_set.append(__UpperCAmelCase				)
                  continue
            for column_index in range(len(__UpperCAmelCase				)				):
                  temp_row.append(first_row[column_index] - row[column_index]				)
            final_set.append(__UpperCAmelCase				)
      # Create next recursion iteration set
      if len(final_set[0]				) != 3:
            SCREAMING_SNAKE_CASE_      		=     final_set[0]
            SCREAMING_SNAKE_CASE_      		=     []
            SCREAMING_SNAKE_CASE_      		=     []
            for row in final_set[1::]:
                  current_first_column.append(row[0]				)
                  next_iteration.append(row[1::]				)
            SCREAMING_SNAKE_CASE_      		=     simplify(__UpperCAmelCase				)
            for i in range(len(__UpperCAmelCase				)				):
                  resultant[i].insert(0     ,     current_first_column[i]				)
            resultant.insert(0     ,     __UpperCAmelCase				)
            SCREAMING_SNAKE_CASE_      		=     resultant
      return final_set

def    UpperCAmelCase_				( __UpperCAmelCase		:      list[list]				)   ->					list:
      if len(__UpperCAmelCase				) == 0:
            raise IndexError('solve_simultaneous() requires n lists of length n+1'				)
      SCREAMING_SNAKE_CASE_      		=     len(__UpperCAmelCase				) + 1
      if any(len(__UpperCAmelCase				) != _length for item in equations				):
            raise IndexError('solve_simultaneous() requires n lists of length n+1'				)
      for row in equations:
            if any(not isinstance(__UpperCAmelCase     ,     (int, float)				) for column in row				):
                  raise ValueError('solve_simultaneous() requires lists of integers'				)
      if len(__UpperCAmelCase				) == 1:
            return [equations[0][-1] / equations[0][0]]
      SCREAMING_SNAKE_CASE_      		=     equations.copy()
      if any(0 in row for row in data_set				):
            SCREAMING_SNAKE_CASE_      		=     data_set.copy()
            SCREAMING_SNAKE_CASE_      		=     []
            for row_index, row in enumerate(__UpperCAmelCase				):
                  if 0 not in row:
                        SCREAMING_SNAKE_CASE_      		=     data_set.pop(__UpperCAmelCase				)
                        break
            if not full_row:
                  raise ValueError('solve_simultaneous() requires at least 1 full equation'				)
            data_set.insert(0     ,     __UpperCAmelCase				)
      SCREAMING_SNAKE_CASE_      		=     data_set.copy()
      SCREAMING_SNAKE_CASE_      		=     simplify(__UpperCAmelCase				)
      SCREAMING_SNAKE_CASE_      		=     simplified[::-1]
      SCREAMING_SNAKE_CASE_      		=     []
      for row in simplified:
            SCREAMING_SNAKE_CASE_      		=     row[-1]
            if not solutions:
                  if row[-2] == 0:
                        solutions.append(0				)
                        continue
                  solutions.append(current_solution / row[-2]				)
                  continue
            SCREAMING_SNAKE_CASE_      		=     row.copy()[: len(__UpperCAmelCase				) - 1 :]
            while temp_row[0] == 0:
                  temp_row.pop(0				)
            if len(__UpperCAmelCase				) == 0:
                  solutions.append(0				)
                  continue
            SCREAMING_SNAKE_CASE_      		=     temp_row[1::]
            SCREAMING_SNAKE_CASE_      		=     temp_row[::-1]
            for column_index, column in enumerate(__UpperCAmelCase				):
                  current_solution -= column * solutions[column_index]
            solutions.append(__UpperCAmelCase				)
      SCREAMING_SNAKE_CASE_      		=     []
      for item in solutions:
            final.append(float(round(__UpperCAmelCase     ,     5				)				)				)
      return final[::-1]


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   lowerCamelCase__					:  List[str]      							=				[
       [2, 1, 1, 1, 1, 4],
       [1, 2, 1, 1, 1, 5],
       [1, 1, 2, 1, 1, 6],
       [1, 1, 1, 2, 1, 7],
       [1, 1, 1, 1, 2, 8],
   ]
   print(solve_simultaneous(eq))
   print(solve_simultaneous([[4, 2]]))





from collections import OrderedDict
from typing import TYPE_CHECKING, Any, List, Mapping, Optional, Union

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import TensorType, logging


if TYPE_CHECKING:
   from ...onnx.config import PatchingSpec
   from ...tokenization_utils_base import PreTrainedTokenizerBase


lowerCamelCase__					:  Optional[int]      							=				logging.get_logger(__name__)

lowerCamelCase__					:  Dict      							=				{
    'allenai/longformer-base-4096': 'https://huggingface.co/allenai/longformer-base-4096/resolve/main/config.json',
    'allenai/longformer-large-4096': 'https://huggingface.co/allenai/longformer-large-4096/resolve/main/config.json',
    'allenai/longformer-large-4096-finetuned-triviaqa': (
        'https://huggingface.co/allenai/longformer-large-4096-finetuned-triviaqa/resolve/main/config.json'
    ),
    'allenai/longformer-base-4096-extra.pos.embd.only': (
        'https://huggingface.co/allenai/longformer-base-4096-extra.pos.embd.only/resolve/main/config.json'
    ),
    'allenai/longformer-large-4096-extra.pos.embd.only': (
        'https://huggingface.co/allenai/longformer-large-4096-extra.pos.embd.only/resolve/main/config.json'
    ),
}





class 			lowerCamelCase_				( _SCREAMING_SNAKE_CASE   ):


 '''simple docstring'''







 lowercase_							       =       "longformer"



 def __init__(				self    :						Union[str, Any]							,							_lowerCAmelCase    :						Union[List[int], int] = 512							,							_lowerCAmelCase    :						int = 2							,							_lowerCAmelCase    :						int = 1							,							_lowerCAmelCase    :						int = 0							,							_lowerCAmelCase    :						int = 2							,							_lowerCAmelCase    :						int = 30_522							,							_lowerCAmelCase    :						int = 768							,							_lowerCAmelCase    :						int = 12							,							_lowerCAmelCase    :						int = 12							,							_lowerCAmelCase    :						int = 3_072							,							_lowerCAmelCase    :						str = "gelu"							,							_lowerCAmelCase    :						float = 0.1							,							_lowerCAmelCase    :						float = 0.1							,							_lowerCAmelCase    :						int = 512							,							_lowerCAmelCase    :						int = 2							,							_lowerCAmelCase    :						float = 0.02							,							_lowerCAmelCase    :						float = 1E-12							,							_lowerCAmelCase    :						bool = False							,							**_lowerCAmelCase    :						Union[str, Any]							,							):
       super().__init__(pad_token_id=_lowerCAmelCase							,							**_lowerCAmelCase		)

       SCREAMING_SNAKE_CASE_      		=     attention_window
       SCREAMING_SNAKE_CASE_      		=     sep_token_id
       SCREAMING_SNAKE_CASE_      		=     bos_token_id
       SCREAMING_SNAKE_CASE_      		=     eos_token_id
       SCREAMING_SNAKE_CASE_      		=     vocab_size
       SCREAMING_SNAKE_CASE_      		=     hidden_size
       SCREAMING_SNAKE_CASE_      		=     num_hidden_layers
       SCREAMING_SNAKE_CASE_      		=     num_attention_heads
       SCREAMING_SNAKE_CASE_      		=     hidden_act
       SCREAMING_SNAKE_CASE_      		=     intermediate_size
       SCREAMING_SNAKE_CASE_      		=     hidden_dropout_prob
       SCREAMING_SNAKE_CASE_      		=     attention_probs_dropout_prob
       SCREAMING_SNAKE_CASE_      		=     max_position_embeddings
       SCREAMING_SNAKE_CASE_      		=     type_vocab_size
       SCREAMING_SNAKE_CASE_      		=     initializer_range
       SCREAMING_SNAKE_CASE_      		=     layer_norm_eps
       SCREAMING_SNAKE_CASE_      		=     onnx_export





class 			lowerCamelCase_				( _SCREAMING_SNAKE_CASE   ):


 '''simple docstring'''







 def __init__(				self    :						Optional[Any]							,							_lowerCAmelCase    :						"PretrainedConfig"							,							_lowerCAmelCase    :						str = "default"							,							_lowerCAmelCase    :						"List[PatchingSpec]" = None		):
       super().__init__(_lowerCAmelCase							,							_lowerCAmelCase							,							_lowerCAmelCase		)
       SCREAMING_SNAKE_CASE_      		=     True



 @property
 def  lowerCAmelCase_    (				self    :						Any		):
       if self.task == "multiple-choice":
             SCREAMING_SNAKE_CASE_      		=     {0: 'batch', 1: 'choice', 2: 'sequence'}
       else:
             SCREAMING_SNAKE_CASE_      		=     {0: 'batch', 1: 'sequence'}
       return OrderedDict(
           [
               ('input_ids', dynamic_axis),
               ('attention_mask', dynamic_axis),
               ('global_attention_mask', dynamic_axis),
           ]		)



 @property
 def  lowerCAmelCase_    (				self    :						Optional[int]		):
       SCREAMING_SNAKE_CASE_      		=     super().outputs
       if self.task == "default":
             SCREAMING_SNAKE_CASE_      		=     {0: 'batch'}
       return outputs



 @property
 def  lowerCAmelCase_    (				self    :						str		):
       return 1E-4



 @property
 def  lowerCAmelCase_    (				self    :						Optional[Any]		):
       # needs to be >= 14 to support tril operator
       return max(super().default_onnx_opset							,							14		)




 def  lowerCAmelCase_    (				self    :						str							,							_lowerCAmelCase    :						"PreTrainedTokenizerBase"							,							_lowerCAmelCase    :						int = -1							,							_lowerCAmelCase    :						int = -1							,							_lowerCAmelCase    :						bool = False							,							_lowerCAmelCase    :						Optional[TensorType] = None							,							):
       SCREAMING_SNAKE_CASE_      		=     super().generate_dummy_inputs(
           preprocessor=_lowerCAmelCase							,							batch_size=_lowerCAmelCase							,							seq_length=_lowerCAmelCase							,							is_pair=_lowerCAmelCase							,							framework=_lowerCAmelCase		)
       import torch

       # for some reason, replacing this code by inputs["global_attention_mask"] = torch.randint(2, inputs["input_ids"].shape, dtype=torch.int64)
       # makes the export fail randomly
       SCREAMING_SNAKE_CASE_      		=     torch.zeros_like(inputs['input_ids']		)
       # make every second token global
       SCREAMING_SNAKE_CASE_      		=     1

       return inputs