
import mpmath  # for roots of unity
import numpy as np
class  lowercase__:



	"""simple docstring"""




	def __init__(       self  :			Dict       ,							SCREAMING_SNAKE_CASE_  :			str=None       ,							SCREAMING_SNAKE_CASE_  :			Tuple=None       )       ->     List[Any]:
					# Input as list
					lowercase_       =					list(poly_a or [0]       )[:]
					lowercase_       =					list(poly_b or [0]       )[:]

					# Remove leading zero coefficients
					while self.polyA[-1] == 0:
									self.polyA.pop()
					lowercase_       =					len(self.polyA       )

					while self.polyB[-1] == 0:
									self.polyB.pop()
					lowercase_       =					len(self.polyB       )

					# Add 0 to make lengths equal a power of 2
					lowercase_       =					int(
					    2 ** np.ceil(np.loga(len(self.polyA       ) + len(self.polyB       ) - 1       )       )       )

					while len(self.polyA       ) < self.c_max_length:
									self.polyA.append(0       )
					while len(self.polyB       ) < self.c_max_length:
									self.polyB.append(0       )
					# A complex root used for the fourier transform
					lowercase_       =					complex(mpmath.root(x=1       ,							n=self.c_max_length       ,							k=1       )       )

					# The product
					lowercase_       =					self.__multiply()
	def 						_lowercase  (       self  :			Optional[int]       ,							SCREAMING_SNAKE_CASE_  :			str       )       ->     List[Any]:
					lowercase_       =					[[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
					# Corner case
					if len(SCREAMING_SNAKE_CASE_       ) <= 1:
									return dft[0]
					#
					lowercase_       =					self.c_max_length // 2
					while next_ncol > 0:
									lowercase_       =					[[] for i in range(SCREAMING_SNAKE_CASE_       )]
									lowercase_       =					self.root**next_ncol

									# First half of next step
									lowercase_       =					1
									for j in range(self.c_max_length // (next_ncol * 2)       ):
													for i in range(SCREAMING_SNAKE_CASE_       ):
																	new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]       )
													current_root *= root
									# Second half of next step
									lowercase_       =					1
									for j in range(self.c_max_length // (next_ncol * 2)       ):
													for i in range(SCREAMING_SNAKE_CASE_       ):
																	new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]       )
													current_root *= root
									# Update
									lowercase_       =					new_dft
									lowercase_       =					next_ncol // 2
					return dft[0]
	def 						_lowercase  (       self  :			int       )       ->     Dict:
					lowercase_       =					self.__dft('''A'''       )
					lowercase_       =					self.__dft('''B'''       )
					lowercase_       =					[[dft_a[i] * dft_b[i] for i in range(self.c_max_length       )]]
					del dft_a
					del dft_b

					# Corner Case
					if len(inverce_c[0]       ) <= 1:
									return inverce_c[0]
					# Inverse DFT
					lowercase_       =					2
					while next_ncol <= self.c_max_length:
									lowercase_       =					[[] for i in range(SCREAMING_SNAKE_CASE_       )]
									lowercase_       =					self.root ** (next_ncol // 2)
									lowercase_       =					1
									# First half of next step
									for j in range(self.c_max_length // next_ncol       ):
													for i in range(next_ncol // 2       ):
																	# Even positions
																	new_inverse_c[i].append(
																	    (
																	        inverce_c[i][j]
																	        + inverce_c[i][j + self.c_max_length // next_ncol]
																	    )
																	    / 2       )
																	# Odd positions
																	new_inverse_c[i + next_ncol // 2].append(
																	    (
																	        inverce_c[i][j]
																	        - inverce_c[i][j + self.c_max_length // next_ncol]
																	    )
																	    / (2 * current_root)       )
													current_root *= root
									# Update
									lowercase_       =					new_inverse_c
									next_ncol *= 2
					# Unpack
					lowercase_       =					[round(x[0].real       ,							8       ) + round(x[0].imag       ,							8       ) * 1J for x in inverce_c]

					# Remove leading 0's
					while inverce_c[-1] == 0:
									inverce_c.pop()
					return inverce_c




	def __str__(       self  :			str       )       ->     Optional[int]:
					lowercase_       =					'''A = ''' + ''' + '''.join(
					    f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]       )       )
					lowercase_       =					'''B = ''' + ''' + '''.join(
					    f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]       )       )
					lowercase_       =					'''A*B = ''' + ''' + '''.join(
					    f'''{coef}*x^{i}''' for coef, i in enumerate(self.product       )       )

					return f'''{a}\n{b}\n{c}'''


# Unit tests
if __name__ == "__main__":
						import doctest

						doctest.testmod()








'''simple docstring'''
def 			a      (			__a ,					__a   )  ->	int:



					'''simple docstring'''






					if len(__a   ) != len(__a   ):
										raise ValueError('''String lengths must match!'''   )

					UpperCamelCase__   :Union[str, Any]												= 0

					for chara, chara in zip(__a ,					__a   ):
										if chara != chara:
															count += 1

					return count


if __name__ == "__main__":
		import doctest

		doctest.testmod()