



from __future__ import annotations

from collections.abc import MutableSequence






class 						__a :



	def __init__(						self							:    int				,	snake_case_							:    List[str]				,	snake_case_							:    str)->							None:





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

						__lowerCAmelCase	   =list(lowercase__)
						__lowerCAmelCase	   =degree



	def __add__(						self							:    Union[str, Any]				,	snake_case_							:    str)->							Polynomial:





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



	def __sub__(						self							:    str				,	snake_case_							:    Tuple)->							Polynomial:
						return self + polynomial_a * Polynomial(0				,	[-1])



	def __neg__(						self							:    Optional[int])->							Polynomial:
						return Polynomial(self.degree				,	[-c for c in self.coefficients])



	def __mul__(						self							:    Optional[Any]				,	snake_case_							:    str)->							Polynomial:
						__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				,	lowercase__)



	def 		UpperCamelCase							(						self							:    Dict				,	snake_case_							:    Any)->							int | float:
						__lowerCAmelCase	   =0
						for i in range(self.degree + 1):
											result += self.coefficients[i] * (substitution**i)
						return result



	def __str__(						self							:    List[str])->							str:
						__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(lowercase__)

						return polynomial



	def __repr__(						self							:    int)->							str:
						return self.__str__()



	def 		UpperCamelCase							(						self							:    Optional[int])->							Polynomial:
						__lowerCAmelCase	   =[0] * self.degree
						for i in range(self.degree):
											__lowerCAmelCase	   =self.coefficients[i + 1] * (i + 1)
						return Polynomial(self.degree - 1				,	lowercase__)



	def 		UpperCamelCase							(						self							:    Optional[Any]				,	snake_case_							:    List[Any] = 0)->							Polynomial:
						__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				,	lowercase__)



	def __eq__(						self							:    Optional[Any]				,	snake_case_							:    str)->							bool:





						if not isinstance(lowercase__				,	lowercase__):
											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							:    str				,	snake_case_							:    str)->							bool:
						return not self.__eq__(lowercase__)









def 					__lowerCAmelCase		(  __lowerCamelCase	:    list[int]	)  ->						int:
					if not numbers:
										return 0

					if not isinstance(__lowerCamelCase				,   (list, tuple)	) or not all(
					    isinstance(__lowerCamelCase				,   __lowerCamelCase	) for number in numbers	):
										raise ValueError("""numbers must be an iterable of integers"""	)

					__lowerCAmelCase	   =__lowerCAmelCase	   =__lowerCAmelCase	   =numbers[0]

					for i in range(1				,   len(__lowerCamelCase	)	):
										# update the maximum and minimum subarray products
										__lowerCAmelCase	   =numbers[i]
										if number < 0:
															__lowerCAmelCase   ,	__lowerCAmelCase	   =min_till_now, max_till_now
										__lowerCAmelCase	   =max(__lowerCamelCase				,   max_till_now * number	)
										__lowerCAmelCase	   =min(__lowerCamelCase				,   min_till_now * number	)

										# update the maximum product found till now
										__lowerCAmelCase	   =max(__lowerCamelCase				,   __lowerCamelCase	)

					return max_prod




