


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

from collections.abc import Callable

lowerCAmelCase   : Dict             =				list[list[float | int]]




def 	_A  (       A							,A							)  ->				str:
	lowercase						:		str   					=		len(__a							)
	lowercase						:		Any   					=		[[0 for _ in range(size + 1							)] for _ in range(__a							)]
	lowercase						:		Optional[int]   					=		4_2
	lowercase						:		Dict   					=		4_2
	lowercase						:		Optional[Any]   					=		4_2
	lowercase						:		List[Any]   					=		4_2
	lowercase						:		Any   					=		4_2
	lowercase						:		Tuple   					=		4_2

	for row in range(__a							):
		for col in range(__a							):
			lowercase						:		Dict   					=		matrix[row][col]

		lowercase						:		int   					=		vector[row][0]

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

		for rowa in range(row + 1							,__a							):
			lowercase						:		str   					=		augmented[rowa][col] / augmented[row][col]
			lowercase						:		Tuple   					=		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							):
			lowercase						:		Optional[int]   					=		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]							,1_0							)] for row in range(__a							)
	]




def 	_A  (       A							)  ->				Dict:
	lowercase						:		Union[str, Any]   					=		len(__a							)
	lowercase						:		List[str]   					=		[[0 for _ in range(__a							)] for _ in range(__a							)]
	lowercase						:		List[str]   					=		[[0] for _ in range(__a							)]
	lowercase						:		Any   					=		4_2
	lowercase						:		Tuple   					=		4_2
	lowercase						:		str   					=		4_2
	lowercase						:		Dict   					=		4_2

	for x_val, y_val in enumerate(__a							):
		for col in range(__a							):
			lowercase						:		Dict   					=		(x_val + 1) ** (size - col - 1)
		lowercase						:		Tuple   					=		y_val

	lowercase						:		List[Any]   					=		solve(__a							,__a							)

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

	return interpolated_func




def 	_A  (       A							)  ->				Optional[Any]:
	return (
	    1
	    - variable
	    + variable**2
	    - variable**3
	    + variable**4
	    - variable**5
	    + variable**6
	    - variable**7
	    + variable**8
	    - variable**9
	    + variable**1_0
	)




def 	_A  (       A = question_function							,A = 1_0							)  ->				Tuple:
	lowercase						:		str   					=		[func(__a							) for x_val in range(1							,order + 1							)]

	lowercase						:		Tuple   					=		[
	    interpolate(data_points[:max_coeff]							) for max_coeff in range(1							,order + 1							)
	]

	lowercase						:		Tuple   					=		0
	lowercase						:		int   					=		4_2
	lowercase						:		Optional[Any]   					=		4_2

	for poly in polynomials:
		lowercase						:		Optional[int]   					=		1
		while func(__a							) == poly(__a							):
			x_val += 1

		ret += poly(__a							)

	return ret


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






import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
	from transformers import AutoModelForSeqaSeqLM, AutoTokenizer




@require_torch
@require_sentencepiece
@require_tokenizers
class       lowercase_					(unittest.TestCase   ):





				@slow
				def 						__UpperCamelCase    (				self)  -> Optional[int]:
											a__      =AutoModelForSeqaSeqLM.from_pretrained('google/mt5-small'       ,  return_dict=lowercase_).to(lowercase_)
											a__      =AutoTokenizer.from_pretrained('google/mt5-small')

											a__      =tokenizer('Hello there'       ,  return_tensors='pt').input_ids
											a__      =tokenizer('Hi I am'       ,  return_tensors='pt').input_ids

											a__      =model(input_ids.to(lowercase_)       ,  labels=labels.to(lowercase_)).loss
											a__      =-(labels.shape[-1] * loss.item())

											a__      =-84.91_27
											self.assertTrue(abs(mtf_score - EXPECTED_SCORE) < 1e-4)

