

from __future__ import annotations

from collections.abc import Callable

a_      =     list[list[float | int]]

def 			lowerCamelCase__			(       _a				,      _a):
	SCREAMING_SNAKE_CASE :   int					  =							len(_a)
	SCREAMING_SNAKE_CASE :   Matrix					  =							[[0 for _ in range(size + 1)] for _ in range(_a)]
	SCREAMING_SNAKE_CASE :   int
	SCREAMING_SNAKE_CASE :   int
	SCREAMING_SNAKE_CASE :   int
	SCREAMING_SNAKE_CASE :   int
	SCREAMING_SNAKE_CASE :   int
	SCREAMING_SNAKE_CASE :   float

	for row in range(_a):
		for col in range(_a):
			SCREAMING_SNAKE_CASE :   List[Any]					  =							matrix[row][col]

		SCREAMING_SNAKE_CASE :   int					  =							vector[row][0]

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

		for rowa in range(row + 1				,      _a):
			SCREAMING_SNAKE_CASE :   Dict					  =							augmented[rowa][col] / augmented[row][col]
			SCREAMING_SNAKE_CASE :   int					  =							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):
			SCREAMING_SNAKE_CASE :   List[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 			lowerCamelCase__			(       _a):
	SCREAMING_SNAKE_CASE :   int					  =							len(_a)
	SCREAMING_SNAKE_CASE :   Matrix					  =							[[0 for _ in range(_a)] for _ in range(_a)]
	SCREAMING_SNAKE_CASE :   Matrix					  =							[[0] for _ in range(_a)]
	SCREAMING_SNAKE_CASE :   Matrix
	SCREAMING_SNAKE_CASE :   int
	SCREAMING_SNAKE_CASE :   int
	SCREAMING_SNAKE_CASE :   int

	for x_val, y_val in enumerate(_a):
		for col in range(_a):
			SCREAMING_SNAKE_CASE :   Any					  =							(x_val + 1) ** (size - col - 1)
		SCREAMING_SNAKE_CASE :   Tuple					  =							y_val

	SCREAMING_SNAKE_CASE :   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 			lowerCamelCase__			(       _a):
	return (
	    1
	    - variable
	    + variable**2
	    - variable**3
	    + variable**4
	    - variable**5
	    + variable**6
	    - variable**7
	    + variable**8
	    - variable**9
	    + variable**10
	)

def 			lowerCamelCase__			(       _a = question_function				,      _a = 10):
	SCREAMING_SNAKE_CASE :   list[int]					  =							[func(_a) for x_val in range(1				,      order + 1)]

	SCREAMING_SNAKE_CASE :   list[Callable[[int], int]]					  =							[
	    interpolate(data_points[:max_coeff]) for max_coeff in range(1				,      order + 1)
	]

	SCREAMING_SNAKE_CASE :   int					  =							0
	SCREAMING_SNAKE_CASE :   Callable[[int], int]
	SCREAMING_SNAKE_CASE :   int

	for poly in polynomials:
		SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							1
		while func(_a) == poly(_a):
			x_val += 1

		ret += poly(_a)

	return ret


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







"""simple docstring"""
import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
			import torch

if is_vision_available():
			from PIL import Image

			from transformers import ViTImageProcessor







class      UpperCamelCase_			(unittest.TestCase	):





	def __init__( self   :					Optional[int]      ,      lowerCAmelCase_   :					Tuple      ,      lowerCAmelCase_   :					List[str]=13      ,      lowerCAmelCase_   :					Union[str, Any]=3      ,      lowerCAmelCase_   :					Union[str, Any]=224      ,      lowerCAmelCase_   :					List[Any]=30      ,      lowerCAmelCase_   :					Any=400      ,      lowerCAmelCase_   :					Any=True      ,      lowerCAmelCase_   :					Dict=None      ,      lowerCAmelCase_   :					int=True      ,      lowerCAmelCase_   :					Any=[0.5, 0.5, 0.5]      ,      lowerCAmelCase_   :					str=[0.5, 0.5, 0.5]      ,      )		->     Dict:
				UpperCAmelCase_	:					int     	=   size if size is not None else {"height": 18, "width": 18}
				UpperCAmelCase_	:					List[Any]     	=   parent
				UpperCAmelCase_	:					int     	=   batch_size
				UpperCAmelCase_	:					Optional[int]     	=   num_channels
				UpperCAmelCase_	:					Dict     	=   image_size
				UpperCAmelCase_	:					Union[str, Any]     	=   min_resolution
				UpperCAmelCase_	:					List[str]     	=   max_resolution
				UpperCAmelCase_	:					Dict     	=   do_resize
				UpperCAmelCase_	:					Optional[int]     	=   size
				UpperCAmelCase_	:					List[str]     	=   do_normalize
				UpperCAmelCase_	:					List[Any]     	=   image_mean
				UpperCAmelCase_	:					Dict     	=   image_std





	def 	_SCREAMING_SNAKE_CASE ( self   :					int		)		->     Union[str, Any]:
				return {
				    "image_mean": self.image_mean,
				    "image_std": self.image_std,
				    "do_normalize": self.do_normalize,
				    "do_resize": self.do_resize,
				    "size": self.size,
				}







@require_torch
@require_vision
class      UpperCamelCase_			(__A							,		unittest.TestCase	):
	__magic_name__       =							ViTImageProcessor if is_vision_available() else None





	def 	_SCREAMING_SNAKE_CASE ( self   :					List[str]		)		->     Optional[Any]:
				UpperCAmelCase_	:					Optional[Any]     	=   EfficientFormerImageProcessorTester(self		)





	@property
	def 	_SCREAMING_SNAKE_CASE ( self   :					Dict		)		->     List[Any]:
				return self.image_proc_tester.prepare_image_processor_dict()





	def 	_SCREAMING_SNAKE_CASE ( self   :					Tuple		)		->     str:
				UpperCAmelCase_	:					Tuple     	=   self.image_processing_class(**self.image_processor_dict		)
				self.assertTrue(hasattr(lowerCAmelCase_      ,      "image_mean"		)		)
				self.assertTrue(hasattr(lowerCAmelCase_      ,      "image_std"		)		)
				self.assertTrue(hasattr(lowerCAmelCase_      ,      "do_normalize"		)		)
				self.assertTrue(hasattr(lowerCAmelCase_      ,      "do_resize"		)		)
				self.assertTrue(hasattr(lowerCAmelCase_      ,      "size"		)		)





	def 	_SCREAMING_SNAKE_CASE ( self   :					List[str]		)		->     List[str]:
				pass





	def 	_SCREAMING_SNAKE_CASE ( self   :					Optional[int]		)		->     int:
				# Initialize image_processor
				UpperCAmelCase_	:					str     	=   self.image_processing_class(**self.image_processor_dict		)
				# create random PIL images
				UpperCAmelCase_	:					int     	=   prepare_image_inputs(self.image_proc_tester      ,      equal_resolution=lowerCAmelCase_		)
				for image in image_inputs:
							self.assertIsInstance(lowerCAmelCase_      ,      Image.Image		)

				# Test not batched input
				UpperCAmelCase_	:					Optional[Any]     	=   image_processor(image_inputs[0]      ,      return_tensors="pt"		).pixel_values
				self.assertEqual(
				    encoded_images.shape      ,      (
				        1,
				        self.image_proc_tester.num_channels,
				        self.image_proc_tester.size["height"],
				        self.image_proc_tester.size["width"],
				    )      ,      )

				# Test batched
				UpperCAmelCase_	:					str     	=   image_processor(lowerCAmelCase_      ,      return_tensors="pt"		).pixel_values
				self.assertEqual(
				    encoded_images.shape      ,      (
				        self.image_proc_tester.batch_size,
				        self.image_proc_tester.num_channels,
				        self.image_proc_tester.size["height"],
				        self.image_proc_tester.size["width"],
				    )      ,      )





	def 	_SCREAMING_SNAKE_CASE ( self   :					Dict		)		->     List[Any]:
				# Initialize image_processor
				UpperCAmelCase_	:					List[str]     	=   self.image_processing_class(**self.image_processor_dict		)
				# create random numpy tensors
				UpperCAmelCase_	:					List[str]     	=   prepare_image_inputs(self.image_proc_tester      ,      equal_resolution=lowerCAmelCase_      ,      numpify=lowerCAmelCase_		)
				for image in image_inputs:
							self.assertIsInstance(lowerCAmelCase_      ,      np.ndarray		)

				# Test not batched input
				UpperCAmelCase_	:					str     	=   image_processor(image_inputs[0]      ,      return_tensors="pt"		).pixel_values
				self.assertEqual(
				    encoded_images.shape      ,      (
				        1,
				        self.image_proc_tester.num_channels,
				        self.image_proc_tester.size["height"],
				        self.image_proc_tester.size["width"],
				    )      ,      )

				# Test batched
				UpperCAmelCase_	:					Dict     	=   image_processor(lowerCAmelCase_      ,      return_tensors="pt"		).pixel_values
				self.assertEqual(
				    encoded_images.shape      ,      (
				        self.image_proc_tester.batch_size,
				        self.image_proc_tester.num_channels,
				        self.image_proc_tester.size["height"],
				        self.image_proc_tester.size["width"],
				    )      ,      )





	def 	_SCREAMING_SNAKE_CASE ( self   :					Optional[int]		)		->     List[Any]:
				# Initialize image_processor
				UpperCAmelCase_	:					Optional[Any]     	=   self.image_processing_class(**self.image_processor_dict		)
				# create random PyTorch tensors
				UpperCAmelCase_	:					Dict     	=   prepare_image_inputs(self.image_proc_tester      ,      equal_resolution=lowerCAmelCase_      ,      torchify=lowerCAmelCase_		)
				for image in image_inputs:
							self.assertIsInstance(lowerCAmelCase_      ,      torch.Tensor		)

				# Test not batched input
				UpperCAmelCase_	:					Optional[int]     	=   image_processor(image_inputs[0]      ,      return_tensors="pt"		).pixel_values
				self.assertEqual(
				    encoded_images.shape      ,      (
				        1,
				        self.image_proc_tester.num_channels,
				        self.image_proc_tester.size["height"],
				        self.image_proc_tester.size["width"],
				    )      ,      )

				# Test batched
				UpperCAmelCase_	:					Optional[int]     	=   image_processor(lowerCAmelCase_      ,      return_tensors="pt"		).pixel_values
				self.assertEqual(
				    encoded_images.shape      ,      (
				        self.image_proc_tester.batch_size,
				        self.image_proc_tester.num_channels,
				        self.image_proc_tester.size["height"],
				        self.image_proc_tester.size["width"],
				    )      ,      )



