






"""simple docstring"""





from __future__ import annotations

from collections.abc import Callable

UpperCamelCase_	:				int										= list[list[float | int]]



def     __lowercase					(    a :				Dict       ,		a :				Dict )					->					Matrix:
						__snake_case      :    int  			=len(a )
						__snake_case      :    Optional[int]  			=[[0 for _ in range(size + 1 )] for _ in range(a )]
						__snake_case      :    Optional[int]  			=42
						__snake_case      :    Union[str, Any]  			=42
						__snake_case      :    List[Any]  			=42
						__snake_case      :    Optional[Any]  			=42
						__snake_case      :    int  			=42
						__snake_case      :    Union[str, Any]  			=42

						for row in range(a ):
												for col in range(a ):
																		__snake_case      :    Union[str, Any]  			=matrix[row][col]

												__snake_case      :    Tuple  			=vector[row][0]

						__snake_case      :    List[Any]  			=0
						__snake_case      :    int  			=0
						while row < size and col < size:
												# pivoting
												__snake_case      :    Optional[Any]  			=max((abs(augmented[rowa][col] ), rowa) for rowa in range(a       ,		a ) )[
												    1
												]
												if augmented[pivot_row][col] == 0:
																		col += 1
																		continue
												else:
																		__snake_case			,				__snake_case      :    Union[str, Any]  			=augmented[pivot_row], augmented[row]

												for rowa in range(row + 1       ,		a ):
																		__snake_case      :    Optional[int]  			=augmented[rowa][col] / augmented[row][col]
																		__snake_case      :    Dict  			=0
																		for cola in range(col + 1       ,		size + 1 ):
																								augmented[rowa][cola] -= augmented[row][cola] * ratio

												row += 1
												col += 1

						# back substitution
						for col in range(1       ,		a ):
												for row in range(a ):
																		__snake_case      :    Union[str, Any]  			=augmented[row][col] / augmented[col][col]
																		for cola in range(a       ,		size + 1 ):
																								augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
						return [
						    [round(augmented[row][size] / augmented[row][row]       ,		10 )] for row in range(a )
						]



def     __lowercase					(    a :				List[str] )					->					Callable[[int], int]:
						__snake_case      :    Optional[Any]  			=len(a )
						__snake_case      :    Tuple  			=[[0 for _ in range(a )] for _ in range(a )]
						__snake_case      :    Dict  			=[[0] for _ in range(a )]
						__snake_case      :    Dict  			=42
						__snake_case      :    Any  			=42
						__snake_case      :    str  			=42
						__snake_case      :    Optional[Any]  			=42

						for x_val, y_val in enumerate(a ):
												for col in range(a ):
																		__snake_case      :    List[str]  			=(x_val + 1) ** (size - col - 1)
												__snake_case      :    Tuple  			=y_val

						__snake_case      :    Optional[int]  			=solve(a       ,		a )

						def interpolated_func(a :				Optional[Any] ) -> int:
												return sum(
												    round(coeffs[x_val][0] ) * (var ** (size - x_val - 1))
												    for x_val in range(a ) )

						return interpolated_func



def     __lowercase					(    a :				Optional[int] )					->					int:
						return (
						    1
						    - variable
						    + variable**2
						    - variable**3
						    + variable**4
						    - variable**5
						    + variable**6
						    - variable**7
						    + variable**8
						    - variable**9
						    + variable**10
						)



def     __lowercase					(    a :				Dict = question_function       ,		a :				Any = 10 )					->					int:
						__snake_case      :    Union[str, Any]  			=[func(a ) for x_val in range(1       ,		order + 1 )]

						__snake_case      :    Union[str, Any]  			=[
						    interpolate(data_points[:max_coeff] ) for max_coeff in range(1       ,		order + 1 )
						]

						__snake_case      :    Optional[int]  			=0
						__snake_case      :    List[Any]  			=42
						__snake_case      :    int  			=42

						for poly in polynomials:
												__snake_case      :    str  			=1
												while func(a ) == poly(a ):
																		x_val += 1

												ret += poly(a )

						return ret


if __name__ == "__main__":
				print(F'''{solution() = }''')










"""simple docstring"""





import unittest

from transformers import MraConfig, is_torch_available
from transformers.testing_utils import require_torch, slow, torch_device

from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_torch_available():
    import torch

    from transformers import (
        MraForMaskedLM,
        MraForMultipleChoice,
        MraForQuestionAnswering,
        MraForSequenceClassification,
        MraForTokenClassification,
        MraModel,
    )
    from transformers.models.mra.modeling_mra import MRA_PRETRAINED_MODEL_ARCHIVE_LIST


class      _lowercase :


      def __init__(    self				:	str							,   a				:	List[str]							,   a				:	Any=2							,   a				:	int=8							,   a				:	List[str]=True							,   a				:	Union[str, Any]=True							,   a				:	Union[str, Any]=True							,   a				:	Optional[int]=True							,   a				:	Union[str, Any]=9_9							,   a				:	Dict=1_6							,   a				:	Union[str, Any]=5							,   a				:	int=2							,   a				:	List[str]=3_6							,   a				:	int="gelu"							,   a				:	Optional[int]=0.0							,   a				:	Any=0.0							,   a				:	Optional[Any]=5_1_2							,   a				:	Tuple=1_6							,   a				:	Dict=2							,   a				:	Union[str, Any]=0.0_2							,   a				:	Dict=3							,   a				:	Union[str, Any]=4							,   a				:	Optional[int]=None							,   ):





            """simple docstring"""







            __snake_case      :    Any  			=parent
            __snake_case      :    int  			=batch_size
            __snake_case      :    Dict  			=seq_length
            __snake_case      :    Any  			=is_training
            __snake_case      :    Optional[int]  			=use_input_mask
            __snake_case      :    List[Any]  			=use_token_type_ids
            __snake_case      :    List[str]  			=use_labels
            __snake_case      :    Optional[Any]  			=vocab_size
            __snake_case      :    Optional[Any]  			=hidden_size
            __snake_case      :    Optional[Any]  			=num_hidden_layers
            __snake_case      :    Any  			=num_attention_heads
            __snake_case      :    Optional[int]  			=intermediate_size
            __snake_case      :    Dict  			=hidden_act
            __snake_case      :    List[str]  			=hidden_dropout_prob
            __snake_case      :    List[Any]  			=attention_probs_dropout_prob
            __snake_case      :    List[str]  			=max_position_embeddings
            __snake_case      :    Tuple  			=type_vocab_size
            __snake_case      :    Tuple  			=type_sequence_label_size
            __snake_case      :    int  			=initializer_range
            __snake_case      :    Any  			=num_labels
            __snake_case      :    List[str]  			=num_choices
            __snake_case      :    Union[str, Any]  			=scope


      def _UpperCamelCase						(    self				:	Dict						):





            """simple docstring"""







            __snake_case      :    Union[str, Any]  			=ids_tensor([self.batch_size, self.seq_length]							,   self.vocab_size						)

            __snake_case      :    int  			=None
            if self.use_input_mask:
                  __snake_case      :    Optional[int]  			=random_attention_mask([self.batch_size, self.seq_length]						)

            __snake_case      :    Optional[Any]  			=None
            if self.use_token_type_ids:
                  __snake_case      :    Optional[int]  			=ids_tensor([self.batch_size, self.seq_length]							,   self.type_vocab_size						)

            __snake_case      :    str  			=None
            __snake_case      :    int  			=None
            __snake_case      :    int  			=None
            if self.use_labels:
                  __snake_case      :    int  			=ids_tensor([self.batch_size]							,   self.type_sequence_label_size						)
                  __snake_case      :    str  			=ids_tensor([self.batch_size, self.seq_length]							,   self.num_labels						)
                  __snake_case      :    Optional[Any]  			=ids_tensor([self.batch_size]							,   self.num_choices						)

            __snake_case      :    List[str]  			=self.get_config()

            return config, input_ids, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels


      def _UpperCamelCase						(    self				:	List[Any]						):





            """simple docstring"""







            return MraConfig(
                vocab_size=self.vocab_size							,   hidden_size=self.hidden_size							,   num_hidden_layers=self.num_hidden_layers							,   num_attention_heads=self.num_attention_heads							,   intermediate_size=self.intermediate_size							,   hidden_act=self.hidden_act							,   hidden_dropout_prob=self.hidden_dropout_prob							,   attention_probs_dropout_prob=self.attention_probs_dropout_prob							,   max_position_embeddings=self.max_position_embeddings							,   type_vocab_size=self.type_vocab_size							,   is_decoder=a							,   initializer_range=self.initializer_range							,   )


      def _UpperCamelCase						(    self				:	List[str]						):





            """simple docstring"""







            __snake_case      :    int  			=self.get_config()
            __snake_case      :    Optional[Any]  			=3_0_0
            return config


      def _UpperCamelCase						(    self				:	Any						):





            """simple docstring"""







            (
                (
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				
            )      :    Tuple  			=self.prepare_config_and_inputs()

            __snake_case      :    Dict  			=True
            __snake_case      :    Any  			=floats_tensor([self.batch_size, self.seq_length, self.hidden_size]						)
            __snake_case      :    Dict  			=ids_tensor([self.batch_size, self.seq_length]							,   vocab_size=2						)

            return (
                config,
                input_ids,
                token_type_ids,
                input_mask,
                sequence_labels,
                token_labels,
                choice_labels,
                encoder_hidden_states,
                encoder_attention_mask,
            )


      def _UpperCamelCase						(    self				:	List[str]							,   a				:	List[Any]							,   a				:	int							,   a				:	Optional[int]							,   a				:	List[Any]							,   a				:	Tuple							,   a				:	Tuple							,   a				:	List[Any]						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=MraModel(config=a						)
            model.to(a						)
            model.eval()
            __snake_case      :    Union[str, Any]  			=model(a							,   attention_mask=a							,   token_type_ids=a						)
            __snake_case      :    Any  			=model(a							,   token_type_ids=a						)
            __snake_case      :    int  			=model(a						)
            self.parent.assertEqual(result.last_hidden_state.shape							,   (self.batch_size, self.seq_length, self.hidden_size)						)


      def _UpperCamelCase						(    self				:	str							,   a				:	Tuple							,   a				:	Any							,   a				:	int							,   a				:	Optional[int]							,   a				:	Union[str, Any]							,   a				:	int							,   a				:	Tuple							,   a				:	Optional[Any]							,   a				:	Optional[int]							,   ):





            """simple docstring"""







            __snake_case      :    Any  			=True
            __snake_case      :    Union[str, Any]  			=MraModel(a						)
            model.to(a						)
            model.eval()
            __snake_case      :    Union[str, Any]  			=model(
                a							,   attention_mask=a							,   token_type_ids=a							,   encoder_hidden_states=a							,   encoder_attention_mask=a							,   )
            __snake_case      :    List[Any]  			=model(
                a							,   attention_mask=a							,   token_type_ids=a							,   encoder_hidden_states=a							,   )
            __snake_case      :    List[str]  			=model(a							,   attention_mask=a							,   token_type_ids=a						)
            self.parent.assertEqual(result.last_hidden_state.shape							,   (self.batch_size, self.seq_length, self.hidden_size)						)


      def _UpperCamelCase						(    self				:	Tuple							,   a				:	Any							,   a				:	List[Any]							,   a				:	int							,   a				:	str							,   a				:	Optional[Any]							,   a				:	List[str]							,   a				:	List[str]						):





            """simple docstring"""







            __snake_case      :    Tuple  			=MraForMaskedLM(config=a						)
            model.to(a						)
            model.eval()
            __snake_case      :    str  			=model(a							,   attention_mask=a							,   token_type_ids=a							,   labels=a						)
            self.parent.assertEqual(result.logits.shape							,   (self.batch_size, self.seq_length, self.vocab_size)						)


      def _UpperCamelCase						(    self				:	List[str]							,   a				:	Optional[int]							,   a				:	int							,   a				:	List[str]							,   a				:	int							,   a				:	Any							,   a				:	Union[str, Any]							,   a				:	Union[str, Any]						):





            """simple docstring"""







            __snake_case      :    Optional[Any]  			=MraForQuestionAnswering(config=a						)
            model.to(a						)
            model.eval()
            __snake_case      :    Dict  			=model(
                a							,   attention_mask=a							,   token_type_ids=a							,   start_positions=a							,   end_positions=a							,   )
            self.parent.assertEqual(result.start_logits.shape							,   (self.batch_size, self.seq_length)						)
            self.parent.assertEqual(result.end_logits.shape							,   (self.batch_size, self.seq_length)						)


      def _UpperCamelCase						(    self				:	Dict							,   a				:	Dict							,   a				:	Dict							,   a				:	Optional[Any]							,   a				:	int							,   a				:	int							,   a				:	List[str]							,   a				:	Any						):





            """simple docstring"""







            __snake_case      :    Optional[Any]  			=self.num_labels
            __snake_case      :    Optional[Any]  			=MraForSequenceClassification(a						)
            model.to(a						)
            model.eval()
            __snake_case      :    str  			=model(a							,   attention_mask=a							,   token_type_ids=a							,   labels=a						)
            self.parent.assertEqual(result.logits.shape							,   (self.batch_size, self.num_labels)						)


      def _UpperCamelCase						(    self				:	Optional[int]							,   a				:	Tuple							,   a				:	Any							,   a				:	Optional[int]							,   a				:	Any							,   a				:	int							,   a				:	str							,   a				:	Optional[int]						):





            """simple docstring"""







            __snake_case      :    Tuple  			=self.num_labels
            __snake_case      :    Optional[int]  			=MraForTokenClassification(config=a						)
            model.to(a						)
            model.eval()
            __snake_case      :    List[str]  			=model(a							,   attention_mask=a							,   token_type_ids=a							,   labels=a						)
            self.parent.assertEqual(result.logits.shape							,   (self.batch_size, self.seq_length, self.num_labels)						)


      def _UpperCamelCase						(    self				:	str							,   a				:	Tuple							,   a				:	Tuple							,   a				:	Optional[Any]							,   a				:	Dict							,   a				:	Dict							,   a				:	Dict							,   a				:	str						):





            """simple docstring"""







            __snake_case      :    Union[str, Any]  			=self.num_choices
            __snake_case      :    Optional[int]  			=MraForMultipleChoice(config=a						)
            model.to(a						)
            model.eval()
            __snake_case      :    List[str]  			=input_ids.unsqueeze(1						).expand(-1							,   self.num_choices							,   -1						).contiguous()
            __snake_case      :    Tuple  			=token_type_ids.unsqueeze(1						).expand(-1							,   self.num_choices							,   -1						).contiguous()
            __snake_case      :    Any  			=input_mask.unsqueeze(1						).expand(-1							,   self.num_choices							,   -1						).contiguous()
            __snake_case      :    int  			=model(
                a							,   attention_mask=a							,   token_type_ids=a							,   labels=a							,   )
            self.parent.assertEqual(result.logits.shape							,   (self.batch_size, self.num_choices)						)







      def _UpperCamelCase						(    self				:	str						):





            """simple docstring"""







            __snake_case      :    Union[str, Any]  			=self.prepare_config_and_inputs()
            (
                (
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				(
                __snake_case
            )			,				
            )      :    Optional[int]  			=config_and_inputs
            __snake_case      :    Tuple  			={'''input_ids''': input_ids, '''token_type_ids''': token_type_ids, '''attention_mask''': input_mask}
            return config, inputs_dict



@require_torch
class      _lowercase (     lowerCAmelCase		,  unittest.TestCase						):
      _a   :     Union[str, Any]								=   (
          (
              MraModel,
              MraForMaskedLM,
              MraForMultipleChoice,
              MraForQuestionAnswering,
              MraForSequenceClassification,
              MraForTokenClassification,
          )
          if is_torch_available()
          else ()
      )
      _a   :     int								=   False
      _a   :     Union[str, Any]								=   False
      _a   :     Dict								=   False
      _a   :     Dict								=   False

      _a   :     Any								=   ()


      def _UpperCamelCase						(    self				:	Optional[int]						):





            """simple docstring"""







            __snake_case      :    Optional[Any]  			=MraModelTester(self						)
            __snake_case      :    List[Any]  			=ConfigTester(self							,   config_class=a							,   hidden_size=3_7						)


      def _UpperCamelCase						(    self				:	List[Any]						):





            """simple docstring"""







            self.config_tester.run_common_tests()


      def _UpperCamelCase						(    self				:	str						):





            """simple docstring"""







            __snake_case      :    Dict  			=self.model_tester.prepare_config_and_inputs()
            self.model_tester.create_and_check_model(*a						)


      def _UpperCamelCase						(    self				:	Any						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=self.model_tester.prepare_config_and_inputs()
            for type in ["absolute", "relative_key", "relative_key_query"]:
                  __snake_case      :    Any  			=type
                  self.model_tester.create_and_check_model(*a						)


      def _UpperCamelCase						(    self				:	Optional[Any]						):





            """simple docstring"""







            __snake_case      :    Optional[Any]  			=self.model_tester.prepare_config_and_inputs()
            self.model_tester.create_and_check_for_masked_lm(*a						)


      def _UpperCamelCase						(    self				:	Dict						):





            """simple docstring"""







            __snake_case      :    Union[str, Any]  			=self.model_tester.prepare_config_and_inputs()
            self.model_tester.create_and_check_for_multiple_choice(*a						)


      def _UpperCamelCase						(    self				:	Dict						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=self.model_tester.prepare_config_and_inputs()
            self.model_tester.create_and_check_for_question_answering(*a						)


      def _UpperCamelCase						(    self				:	int						):





            """simple docstring"""







            __snake_case      :    str  			=self.model_tester.prepare_config_and_inputs()
            self.model_tester.create_and_check_for_sequence_classification(*a						)


      def _UpperCamelCase						(    self				:	str						):





            """simple docstring"""







            __snake_case      :    Union[str, Any]  			=self.model_tester.prepare_config_and_inputs()
            self.model_tester.create_and_check_for_token_classification(*a						)


      @slow
      def _UpperCamelCase						(    self				:	Tuple						):





            """simple docstring"""







            for model_name in MRA_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
                  __snake_case      :    Tuple  			=MraModel.from_pretrained(a						)
                  self.assertIsNotNone(a						)







      @unittest.skip(reason='''MRA does not output attentions'''						)
      def _UpperCamelCase						(    self				:	Optional[Any]						):





            """simple docstring"""







            return



@require_torch
class      _lowercase (     unittest.TestCase						):


      @slow
      def _UpperCamelCase						(    self				:	Dict						):





            """simple docstring"""







            __snake_case      :    str  			=MraModel.from_pretrained('''uw-madison/mra-base-512-4'''						)
            __snake_case      :    Optional[int]  			=torch.arange(2_5_6						).unsqueeze(0						)

            with torch.no_grad():
                  __snake_case      :    List[str]  			=model(a						)[0]

            __snake_case      :    Any  			=torch.Size((1, 2_5_6, 7_6_8)						)
            self.assertEqual(output.shape							,   a						)

            __snake_case      :    int  			=torch.tensor(
                [[[-0.0_1_4_0, 0.0_8_3_0, -0.0_3_8_1], [0.1_5_4_6, 0.1_4_0_2, 0.0_2_2_0], [0.1_1_6_2, 0.0_8_5_1, 0.0_1_6_5]]]						)

            self.assertTrue(torch.allclose(output[:, :3, :3]							,   a							,   atol=1e-4						)						)


      @slow
      def _UpperCamelCase						(    self				:	List[str]						):





            """simple docstring"""







            __snake_case      :    Any  			=MraForMaskedLM.from_pretrained('''uw-madison/mra-base-512-4'''						)
            __snake_case      :    Union[str, Any]  			=torch.arange(2_5_6						).unsqueeze(0						)

            with torch.no_grad():
                  __snake_case      :    Optional[int]  			=model(a						)[0]

            __snake_case      :    Union[str, Any]  			=5_0_2_6_5

            __snake_case      :    List[str]  			=torch.Size((1, 2_5_6, vocab_size)						)
            self.assertEqual(output.shape							,   a						)

            __snake_case      :    str  			=torch.tensor(
                [[[9.2_5_9_5, -3.6_0_3_8, 1_1.8_8_1_9], [9.3_8_6_9, -3.2_6_9_3, 1_1.0_9_5_6], [1_1.8_5_2_4, -3.4_9_3_8, 1_3.1_2_1_0]]]						)

            self.assertTrue(torch.allclose(output[:, :3, :3]							,   a							,   atol=1e-4						)						)







      @slow
      def _UpperCamelCase						(    self				:	Tuple						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=MraForMaskedLM.from_pretrained('''uw-madison/mra-base-4096-8-d3'''						)
            __snake_case      :    Optional[int]  			=torch.arange(4_0_9_6						).unsqueeze(0						)

            with torch.no_grad():
                  __snake_case      :    Tuple  			=model(a						)[0]

            __snake_case      :    Optional[int]  			=5_0_2_6_5

            __snake_case      :    Tuple  			=torch.Size((1, 4_0_9_6, vocab_size)						)
            self.assertEqual(output.shape							,   a						)

            __snake_case      :    List[str]  			=torch.tensor(
                [[[5.4_7_8_9, -2.3_5_6_4, 7.5_0_6_4], [7.9_0_6_7, -1.3_3_6_9, 9.9_6_6_8], [9.0_7_1_2, -1.8_1_0_6, 7.0_3_8_0]]]						)

            self.assertTrue(torch.allclose(output[:, :3, :3]							,   a							,   atol=1e-4						)						)


