





from __future__ import annotations

from collections.abc import MutableSequence

class   lowerCAmelCase				:
 def __init__( self    : Any     ,	UpperCAmelCase    : int     ,	UpperCAmelCase    : MutableSequence[float]      )     ->      None:
     if len(UpperCAmelCase      ) != degree + 1:
         raise ValueError(
             'The number of coefficients should be equal to the degree + 1.'      )

     lowerCamelCase__       : list[float]   					=						list(UpperCAmelCase      )
     lowerCamelCase__       : int   					=						degree
 def __add__( self    : Any     ,	UpperCAmelCase    : Polynomial      )     ->      Polynomial:

     if self.degree > polynomial_a.degree:
         lowerCamelCase__       : Union[str, Any]   					=						self.coefficients[:]
         for i in range(polynomial_a.degree + 1      ):
             coefficients[i] += polynomial_a.coefficients[i]
         return Polynomial(self.degree     ,	UpperCAmelCase      )
     else:
         lowerCamelCase__       : Union[str, Any]   					=						polynomial_a.coefficients[:]
         for i in range(self.degree + 1      ):
             coefficients[i] += self.coefficients[i]
         return Polynomial(polynomial_a.degree     ,	UpperCAmelCase      )
 def __sub__( self    : List[str]     ,	UpperCAmelCase    : Polynomial      )     ->      Polynomial:
     return self + polynomial_a * Polynomial(0     ,	[-1]      )
 def __neg__( self    : str      )     ->      Polynomial:
     return Polynomial(self.degree     ,	[-c for c in self.coefficients]      )
 def __mul__( self    : Optional[int]     ,	UpperCAmelCase    : Polynomial      )     ->      Polynomial:
     lowerCamelCase__       : list[float]   					=						[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     ,	UpperCAmelCase      )
 def 	A_      ( self    : int     ,	UpperCAmelCase    : int | float      )     ->      int | float:
     lowerCamelCase__       : int | float   					=						0
     for i in range(self.degree + 1      ):
         result += self.coefficients[i] * (substitution**i)
     return result
 def __str__( self    : Optional[Any]      )     ->      str:
     lowerCamelCase__       : Union[str, Any]   					=						''
     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(UpperCAmelCase      )

     return polynomial
 def __repr__( self    : Optional[Any]      )     ->      str:
     return self.__str__()
 def 	A_      ( self    : Optional[int]      )     ->      Polynomial:
     lowerCamelCase__       : list[float]   					=						[0] * self.degree
     for i in range(self.degree      ):
         lowerCamelCase__       : List[str]   					=						self.coefficients[i + 1] * (i + 1)
     return Polynomial(self.degree - 1     ,	UpperCAmelCase      )
 def 	A_      ( self    : Optional[Any]     ,	UpperCAmelCase    : int | float = 0      )     ->      Polynomial:
     lowerCamelCase__       : list[float]   					=						[0] * (self.degree + 2)
     lowerCamelCase__       : List[str]   					=						constant
     for i in range(self.degree + 1      ):
         lowerCamelCase__       : Tuple   					=						self.coefficients[i] / (i + 1)
     return Polynomial(self.degree + 1     ,	UpperCAmelCase      )
 def __eq__( self    : Any     ,	UpperCAmelCase    : object      )     ->      bool:
     if not isinstance(UpperCAmelCase     ,	UpperCAmelCase      ):
         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    : List[Any]     ,	UpperCAmelCase    : object      )     ->      bool:
     return not self.__eq__(UpperCAmelCase      )












def 			SCREAMING_SNAKE_CASE (			_UpperCAmelCase = 200					)     ->	int:
    lowerCamelCase__       : Dict   					=						[1, 2, 5, 10, 20, 50, 100, 200]
    lowerCamelCase__       : Union[str, Any]   					=						[0] * (pence + 1)
    lowerCamelCase__       : List[str]   					=						1  # base case: 1 way to make 0 pence

    for coin in coins:
        for i in range(_UpperCAmelCase		,      pence + 1		,      1					):
            number_of_ways[i] += number_of_ways[i - coin]
    return number_of_ways[pence]


if __name__ == "__main__":
    assert solution(2_00) == 7_36_82





