





from __future__ import annotations

from collections.abc import MutableSequence






class 					__A    :

			'''simple docstring'''







			def __init__(    self       ,  __lowerCAmelCase       ,  __lowerCAmelCase							):



				'''simple docstring'''







				if len(__lowerCAmelCase							) != degree + 1:
					raise ValueError(
					    '''The number of coefficients should be equal to the degree + 1.'''							)

				lowerCamelCase__								=		list(__lowerCAmelCase							)
				lowerCamelCase__								=		degree





			def __add__(    self       ,  __lowerCAmelCase							):



				'''simple docstring'''







				if self.degree > polynomial_a.degree:
					lowerCamelCase__								=		self.coefficients[:]
					for i in range(polynomial_a.degree + 1							):
						coefficients[i] += polynomial_a.coefficients[i]
					return Polynomial(self.degree       ,  __lowerCAmelCase							)
				else:
					lowerCamelCase__								=		polynomial_a.coefficients[:]
					for i in range(self.degree + 1							):
						coefficients[i] += self.coefficients[i]
					return Polynomial(polynomial_a.degree       ,  __lowerCAmelCase							)





			def __sub__(    self       ,  __lowerCAmelCase							):



				'''simple docstring'''







				return self + polynomial_a * Polynomial(0       ,  [-1]							)





			def __neg__(    self							):



				'''simple docstring'''







				return Polynomial(self.degree       ,  [-c for c in self.coefficients]							)





			def __mul__(    self       ,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__								=		[0] * (self.degree + polynomial_a.degree + 1)
				for i in range(self.degree + 1							):
					for j in range(polynomial_a.degree + 1							):
						coefficients[i + j] += (
						    self.coefficients[i] * polynomial_a.coefficients[j]
						)

				return Polynomial(self.degree + polynomial_a.degree       ,  __lowerCAmelCase							)





			def 		__lowerCamelCase				(    self       ,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__								=		0
				for i in range(self.degree + 1							):
					result += self.coefficients[i] * (substitution**i)
				return result





			def __str__(    self							):



				'''simple docstring'''







				lowerCamelCase__								=		''''''
				for i in range(self.degree       ,  -1       ,  -1							):
					if self.coefficients[i] == 0:
						continue
					elif self.coefficients[i] > 0:
						if polynomial:
							polynomial += " + "
					else:
						polynomial += " - "

					if i == 0:
						polynomial += str(abs(self.coefficients[i]							)							)
					elif i == 1:
						polynomial += str(abs(self.coefficients[i]							)							) + "x"
					else:
						polynomial += str(abs(self.coefficients[i]							)							) + "x^" + str(__lowerCAmelCase							)

				return polynomial





			def __repr__(    self							):



				'''simple docstring'''







				return self.__str__()





			def 		__lowerCamelCase				(    self							):



				'''simple docstring'''







				lowerCamelCase__								=		[0] * self.degree
				for i in range(self.degree							):
					lowerCamelCase__								=		self.coefficients[i + 1] * (i + 1)
				return Polynomial(self.degree - 1       ,  __lowerCAmelCase							)





			def 		__lowerCamelCase				(    self       ,  __lowerCAmelCase = 0							):



				'''simple docstring'''







				lowerCamelCase__								=		[0] * (self.degree + 2)
				lowerCamelCase__								=		constant
				for i in range(self.degree + 1							):
					lowerCamelCase__								=		self.coefficients[i] / (i + 1)
				return Polynomial(self.degree + 1       ,  __lowerCAmelCase							)





			def __eq__(    self       ,  __lowerCAmelCase							):



				'''simple docstring'''







				if not isinstance(__lowerCAmelCase       ,  __lowerCAmelCase							):
					return False

				if self.degree != polynomial_a.degree:
					return False

				for i in range(self.degree + 1							):
					if self.coefficients[i] != polynomial_a.coefficients[i]:
						return False

				return True





			def __ne__(    self       ,  __lowerCAmelCase							):



				'''simple docstring'''







				return not self.__eq__(__lowerCAmelCase							)










import unittest

from transformers.utils.backbone_utils import (
    BackboneMixin,
    get_aligned_output_features_output_indices,
    verify_out_features_out_indices,
)


class   A			(unittest.TestCase    ):
			'''simple docstring'''




			def    a_       (			self   :    Any   )	->	Union[str, Any]:







					"""simple docstring"""






					A__        =   ["""a""", """b""", """c"""]

					# Defaults to last layer if both are None
					A__      ,			A__        =   get_aligned_output_features_output_indices(__lowerCAmelCase							,	__lowerCAmelCase							,	__lowerCAmelCase   )
					self.assertEqual(__lowerCAmelCase							,	["""c"""]   )
					self.assertEqual(__lowerCAmelCase							,	[2]   )

					# Out indices set to match out features
					A__      ,			A__        =   get_aligned_output_features_output_indices(["""a""", """c"""]							,	__lowerCAmelCase							,	__lowerCAmelCase   )
					self.assertEqual(__lowerCAmelCase							,	["""a""", """c"""]   )
					self.assertEqual(__lowerCAmelCase							,	[0, 2]   )

					# Out features set to match out indices
					A__      ,			A__        =   get_aligned_output_features_output_indices(__lowerCAmelCase							,	[0, 2]							,	__lowerCAmelCase   )
					self.assertEqual(__lowerCAmelCase							,	["""a""", """c"""]   )
					self.assertEqual(__lowerCAmelCase							,	[0, 2]   )

					# Out features selected from negative indices
					A__      ,			A__        =   get_aligned_output_features_output_indices(__lowerCAmelCase							,	[-3, -1]							,	__lowerCAmelCase   )
					self.assertEqual(__lowerCAmelCase							,	["""a""", """c"""]   )
					self.assertEqual(__lowerCAmelCase							,	[-3, -1]   )






			def    a_       (			self   :    Optional[Any]   )	->	Optional[Any]:







					"""simple docstring"""






					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(["""a""", """b"""]							,	(0, 1)							,	__lowerCAmelCase   )

					# Out features must be a list
					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(("""a""", """b""")							,	(0, 1)							,	["""a""", """b"""]   )

					# Out features must be a subset of stage names
					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(["""a""", """b"""]							,	(0, 1)							,	["""a"""]   )

					# Out indices must be a list or tuple
					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(__lowerCAmelCase							,	0							,	["""a""", """b"""]   )

					# Out indices must be a subset of stage names
					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(__lowerCAmelCase							,	(0, 1)							,	["""a"""]   )

					# Out features and out indices must be the same length
					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(["""a""", """b"""]							,	(0,)							,	["""a""", """b""", """c"""]   )

					# Out features should match out indices
					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(["""a""", """b"""]							,	(0, 2)							,	["""a""", """b""", """c"""]   )

					# Out features and out indices should be in order
					with self.assertRaises(__lowerCAmelCase   ):
							verify_out_features_out_indices(["""b""", """a"""]							,	(0, 1)							,	["""a""", """b"""]   )

					# Check passes with valid inputs
					verify_out_features_out_indices(["""a""", """b""", """d"""]							,	(0, 1, -1)							,	["""a""", """b""", """c""", """d"""]   )







			def    a_       (			self   :    Union[str, Any]   )	->	List[str]:







					"""simple docstring"""






					A__        =   BackboneMixin()

					A__        =   ["""a""", """b""", """c"""]
					A__        =   ["""a""", """c"""]
					A__        =   [0, 2]

					# Check that the output features and indices are set correctly
					self.assertEqual(backbone.out_features							,	["""a""", """c"""]   )
					self.assertEqual(backbone.out_indices							,	[0, 2]   )

					# Check out features and indices are updated correctly
					A__        =   ["""a""", """b"""]
					self.assertEqual(backbone.out_features							,	["""a""", """b"""]   )
					self.assertEqual(backbone.out_indices							,	[0, 1]   )

					A__        =   [-3, -1]
					self.assertEqual(backbone.out_features							,	["""a""", """c"""]   )
					self.assertEqual(backbone.out_indices							,	[-3, -1]   )



