



from __future__ import annotations

from collections.abc import MutableSequence

class    _A	:



       def __init__(		self							:					Optional[Any]					,		__SCREAMING_SNAKE_CASE							:					int					,		__SCREAMING_SNAKE_CASE							:					MutableSequence[float]):


           '''simple docstring'''

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

           __a							=    list(__SCREAMING_SNAKE_CASE)
           __a							=    degree



       def __add__(		self							:					str					,		__SCREAMING_SNAKE_CASE							:					Polynomial):


           '''simple docstring'''

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



       def __sub__(		self							:					Dict					,		__SCREAMING_SNAKE_CASE							:					Polynomial):


           '''simple docstring'''

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



       def __neg__(		self							:					str):


           '''simple docstring'''

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



       def __mul__(		self							:					str					,		__SCREAMING_SNAKE_CASE							:					Polynomial):


           '''simple docstring'''

           __a							=    [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					,		__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase      (		self							:					Optional[Any]					,		__SCREAMING_SNAKE_CASE							:					int | float):


           '''simple docstring'''

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



       def __str__(		self							:					List[Any]):


           '''simple docstring'''

           __a							=    ''''''
           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(__SCREAMING_SNAKE_CASE)

           return polynomial



       def __repr__(		self							:					List[Any]):


           '''simple docstring'''

           return self.__str__()



       def 		_lowerCamelCase      (		self							:					List[Any]):


           '''simple docstring'''

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



       def 		_lowerCamelCase      (		self							:					List[Any]					,		__SCREAMING_SNAKE_CASE							:					int | float = 0):


           '''simple docstring'''

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



       def __eq__(		self							:					List[Any]					,		__SCREAMING_SNAKE_CASE							:					object):


           '''simple docstring'''

           if not isinstance(__SCREAMING_SNAKE_CASE					,		__SCREAMING_SNAKE_CASE):
               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							:					Optional[int]					,		__SCREAMING_SNAKE_CASE							:					object):


           '''simple docstring'''

           return not self.__eq__(__SCREAMING_SNAKE_CASE)










# Lint as: python3
import itertools
import os
import re


__snake_case						:int						=					re.compile(r'''([A-Z]+)([A-Z][a-z])''')
__snake_case						:List[Any]						=					re.compile(r'''([a-z\d])([A-Z])''')

__snake_case						:Dict						=					re.compile(r'''(?<!_)_(?!_)''')
__snake_case						:Optional[int]						=					re.compile(r'''(_{2,})''')

__snake_case						:Optional[Any]						=					r'''^\w+(\.\w+)*$'''

__snake_case						:Union[str, Any]						=					r'''<>:/\|?*'''





def 					__snake_case     (      _UpperCAmelCase    ):
    __a							=    _uppercase_uppercase_re.sub(R'''\1_\2'''       ,			_UpperCAmelCase    )
    __a							=    _lowercase_uppercase_re.sub(R'''\1_\2'''       ,			_UpperCAmelCase    )
    return name.lower()





def 					__snake_case     (      _UpperCAmelCase    ):
    __a							=    _single_underscore_re.split(_UpperCAmelCase    )
    __a							=    [_multiple_underscores_re.split(_UpperCAmelCase    ) for n in name]
    return "".join(n.capitalize() for n in itertools.chain.from_iterable(_UpperCAmelCase    ) if n != ''''''    )





def 					__snake_case     (      _UpperCAmelCase    ):
    if os.path.basename(_UpperCAmelCase    ) != name:
        raise ValueError(f'Should be a dataset name, not a path: {name}'    )
    return camelcase_to_snakecase(_UpperCAmelCase    )





def 					__snake_case     (      _UpperCAmelCase       ,			_UpperCAmelCase    ):
    if os.path.basename(_UpperCAmelCase    ) != name:
        raise ValueError(f'Should be a dataset name, not a path: {name}'    )
    if not re.match(_split_re       ,			_UpperCAmelCase    ):
        raise ValueError(f'Split name should match \'{_split_re}\'\' but got \'{split}\'.'    )
    return f'{filename_prefix_for_name(_UpperCAmelCase    )}-{split}'





def 					__snake_case     (      _UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase=None    ):
    __a							=    filename_prefix_for_split(_UpperCAmelCase       ,			_UpperCAmelCase    )
    if filetype_suffix:
        prefix += f'.{filetype_suffix}'
    __a							=    os.path.join(_UpperCAmelCase       ,			_UpperCAmelCase    )
    return f'{filepath}*'





def 					__snake_case     (      _UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase=None       ,			_UpperCAmelCase=None    ):
    __a							=    filename_prefix_for_split(_UpperCAmelCase       ,			_UpperCAmelCase    )
    __a							=    os.path.join(_UpperCAmelCase       ,			_UpperCAmelCase    )

    if shard_lengths:
        __a							=    len(_UpperCAmelCase    )
        __a							=    [f'{prefix}-{shard_id:05d}-of-{num_shards:05d}' for shard_id in range(_UpperCAmelCase    )]
        if filetype_suffix:
            __a							=    [filename + f'.{filetype_suffix}' for filename in filenames]
        return filenames
    else:
        __a							=    prefix
        if filetype_suffix:
            filename += f'.{filetype_suffix}'
        return [filename]





