
from __future__ import annotations







class        lowercase	:




							def __init__(       self     ,A__):
												lowercase					=		order

												# a_{0} ... a_{k}
												lowercase					=		[1.0] + [0.0] * order
												# b_{0} ... b_{k}
												lowercase					=		[1.0] + [0.0] * order

												# x[n-1] ... x[n-k]
												lowercase					=		[0.0] * self.order
												# y[n-1] ... y[n-k]
												lowercase					=		[0.0] * self.order




							def 				A__   (       self     ,A__     ,A__):
												if len(A__) < self.order:
																	lowercase					=		[1.0, *a_coeffs]

												if len(A__) != self.order + 1:
																	lowercase					=		(
																	    f'Expected a_coeffs to have {self.order + 1} elements '
																	    f'for {self.order}-order filter, got {len(A__)}'
																	)
																	raise ValueError(A__)

												if len(A__) != self.order + 1:
																	lowercase					=		(
																	    f'Expected b_coeffs to have {self.order + 1} elements '
																	    f'for {self.order}-order filter, got {len(A__)}'
																	)
																	raise ValueError(A__)

												lowercase					=		a_coeffs
												lowercase					=		b_coeffs





							def 				A__   (       self     ,A__):
												lowercase					=		0.0

												# Start at index 1 and do index 0 at the end.
												for i in range(1     ,self.order + 1):
																	result += (
																	    self.b_coeffs[i] * self.input_history[i - 1]
																	    - self.a_coeffs[i] * self.output_history[i - 1]
																	)

												lowercase					=		(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

												lowercase					=		self.input_history[:-1]
												lowercase					=		self.output_history[:-1]

												lowercase					=		sample
												lowercase					=		result

												return result






class        lowercase	:




							def __init__(       self     ,A__):
												lowercase					=		val
												lowercase					=		None
												lowercase					=		None





							def 				A__   (       self     ,A__):
												if self.val:
																	if val < self.val:
																						if self.left is None:
																											lowercase					=		Node(A__)
																						else:
																											self.left.insert(A__)
																	elif val > self.val:
																						if self.right is None:
																											lowercase					=		Node(A__)
																						else:
																											self.right.insert(A__)
												else:
																	lowercase					=		val



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					# Recursive traversal
					if root:
										inorder(root.left				,    lowerCAmelCase__	)
										res.append(root.val	)
										inorder(root.right				,    lowerCAmelCase__	)



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					# Build BST
					if len(lowerCAmelCase__	) == 0:
										return arr
					lowercase					=		Node(arr[0]	)
					for i in range(1				,    len(lowerCAmelCase__	)	):
										root.insert(arr[i]	)
					# Traverse BST in order.
					lowercase					=		[]
					inorder(lowerCAmelCase__				,    lowerCAmelCase__	)
					return res


if __name__ == "__main__":
							print(tree_sort([10, 1, 3, 2, 9, 14, 13]))




