



def        A       (      _lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							return x if y == 0 else greatest_common_divisor(_lowerCamelCase       ,				x % y						)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							return (x * y) // greatest_common_divisor(_lowerCamelCase       ,				_lowerCamelCase						)






def        A       (      _lowerCamelCase = 20						):





							'''simple docstring'''




							_lowerCAmelCase  :							Optional[int]				     =					1
							for i in range(1       ,				n + 1						):
														_lowerCAmelCase  :							str				     =					lcm(_lowerCamelCase       ,				_lowerCamelCase						)
							return g


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





from __future__ import annotations

from collections.abc import MutableSequence



class 						UpperCAmelCase_					:







							def __init__(     self,    __a,    __a):

														'''simple docstring'''

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

														_lowerCAmelCase  :							list[float]				     =					list(__a)
														_lowerCAmelCase  :							Any				     =					degree







							def __add__(     self,    __a):

														'''simple docstring'''

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







							def __sub__(     self,    __a):

														'''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,    __a):

														'''simple docstring'''

														_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,    __a)







							def      snake_case__   (     self,    __a):

														'''simple docstring'''

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







							def __str__(     self):

														'''simple docstring'''

														_lowerCAmelCase  :							List[str]				     =					""
														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(__a)

														return polynomial







							def __repr__(     self):

														'''simple docstring'''

														return self.__str__()







							def      snake_case__   (     self):

														'''simple docstring'''

														_lowerCAmelCase  :							list[float]				     =					[0] * self.degree
														for i in range(self.degree):
																					_lowerCAmelCase  :							List[Any]				     =					self.coefficients[i + 1] * (i + 1)
														return Polynomial(self.degree - 1,    __a)







							def      snake_case__   (     self,    __a = 0):

														'''simple docstring'''

														_lowerCAmelCase  :							list[float]				     =					[0] * (self.degree + 2)
														_lowerCAmelCase  :							Optional[Any]				     =					constant
														for i in range(self.degree + 1):
																					_lowerCAmelCase  :							Dict				     =					self.coefficients[i] / (i + 1)
														return Polynomial(self.degree + 1,    __a)







							def __eq__(     self,    __a):

														'''simple docstring'''

														if not isinstance(__a,    __a):
																					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,    __a):

														'''simple docstring'''

														return not self.__eq__(__a)
