


"""simple docstring"""
class      _UpperCAmelCase					:






		'''simple docstring'''

		def __init__(self							,			a_   ):





			'''simple docstring'''

			__snake_case      :		List[Any]         =							val
			# Number of nodes in left subtree
			__snake_case      :		Dict         =							0
			__snake_case      :		Optional[Any]         =							None
			__snake_case      :		Dict         =							None
			__snake_case      :		List[Any]         =							None



		def 							SCREAMING_SNAKE_CASE    (self							,			a_   ):





			'''simple docstring'''

			assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

			if self.val < other.val:
				__snake_case      :		str         =							self.right
				__snake_case      :		Union[str, Any]         =							None
				if self.right:
					__snake_case      :		List[Any]         =							other
				__snake_case      :		Optional[int]         =							other
				__snake_case      :		Union[str, Any]         =							self.left_tree_size * 2 + 1
				return self
			else:
				__snake_case      :		Optional[Any]         =							other.right
				__snake_case      :		Any         =							None
				if other.right:
					__snake_case      :		Union[str, Any]         =							self
				__snake_case      :		int         =							self
				__snake_case      :		List[Any]         =							other.left_tree_size * 2 + 1
				return other



class      _UpperCAmelCase					:






		'''simple docstring'''

		def __init__(self							,			a_=None							,			a_=None							,			a_=0   ):





			'''simple docstring'''

			__snake_case      :		str         =							heap_size
			__snake_case      :		Optional[int]         =							bottom_root
			__snake_case      :		Any         =							min_node



		def 							SCREAMING_SNAKE_CASE    (self							,			a_   ):





			'''simple docstring'''

			if other.size == 0:
				return None
			if self.size == 0:
				__snake_case      :		Any         =							other.size
				__snake_case      :		str         =							other.bottom_root
				__snake_case      :		Optional[int]         =							other.min_node
				return None
			# Update size
			__snake_case      :		List[str]         =							self.size + other.size

			# Update min.node
			if self.min_node.val > other.min_node.val:
				__snake_case      :		Dict         =							other.min_node
			# Merge

			# Order roots by left_subtree_size
			__snake_case      :		Optional[int]         =							[]
			__snake_case      ,				__snake_case      :		List[str]         =							self.bottom_root, other.bottom_root
			while i or j:
				if i and ((not j) or i.left_tree_size < j.left_tree_size):
					combined_roots_list.append((i, True)   )
					__snake_case      :		Optional[Any]         =							i.parent
				else:
					combined_roots_list.append((j, False)   )
					__snake_case      :		List[str]         =							j.parent
        # Insert links between them
			for i in range(len(a_   ) - 1   ):
				if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
					__snake_case      :		List[Any]         =							combined_roots_list[i + 1][0]
					__snake_case      :		Optional[Any]         =							combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
			__snake_case      :		List[Any]         =							combined_roots_list[0][0]
			while i.parent:
				if (
				    (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
				) or (
				    i.left_tree_size == i.parent.left_tree_size
				    and i.left_tree_size != i.parent.parent.left_tree_size
				):
					# Neighbouring Nodes
					__snake_case      :		Union[str, Any]         =							i.left
					__snake_case      :		int         =							i.parent.parent

					# Merging trees
					__snake_case      :		Optional[Any]         =							i.merge_trees(i.parent   )

					# Updating links
					__snake_case      :		Dict         =							previous_node
					__snake_case      :		Optional[Any]         =							next_node
					if previous_node:
						__snake_case      :		List[str]         =							i
					if next_node:
						__snake_case      :		Any         =							i
				else:
					__snake_case      :		Optional[Any]         =							i.parent
        # Updating self.bottom_root
			while i.left:
				__snake_case      :		Union[str, Any]         =							i.left
			__snake_case      :		int         =							i

			# Update other
			__snake_case      :		Tuple         =							self.size
			__snake_case      :		Optional[int]         =							self.bottom_root
			__snake_case      :		List[str]         =							self.min_node

			# Return the merged heap
			return self



		def 							SCREAMING_SNAKE_CASE    (self							,			a_   ):





			'''simple docstring'''

			if self.size == 0:
				__snake_case      :		str         =							Node(a_   )
				__snake_case      :		List[Any]         =							1
				__snake_case      :		Optional[Any]         =							self.bottom_root
			else:
				# Create new node
				__snake_case      :		List[Any]         =							Node(a_   )

				# Update size
				self.size += 1

				# update min_node
				if val < self.min_node.val:
					__snake_case      :		Union[str, Any]         =							new_node
				# Put new_node as a bottom_root in heap
				__snake_case      :		str         =							new_node
				__snake_case      :		List[str]         =							self.bottom_root
				__snake_case      :		List[Any]         =							new_node

				# Consecutively merge roots with same left_tree_size
				while (
				    self.bottom_root.parent
				    and self.bottom_root.left_tree_size
				    == self.bottom_root.parent.left_tree_size
				):
					# Next node
					__snake_case      :		Optional[int]         =							self.bottom_root.parent.parent

					# Merge
					__snake_case      :		List[Any]         =							self.bottom_root.merge_trees(self.bottom_root.parent   )

					# Update Links
					__snake_case      :		List[Any]         =							next_node
					__snake_case      :		Optional[Any]         =							None
					if next_node:
						__snake_case      :		List[Any]         =							self.bottom_root



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			return self.min_node.val



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			return self.size == 0



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			__snake_case      :		List[Any]         =							self.min_node.val

			# Last element in heap corner case
			if self.size == 1:
				# Update size
				__snake_case      :		Union[str, Any]         =							0

				# Update bottom root
				__snake_case      :		Tuple         =							None

				# Update min_node
				__snake_case      :		Optional[int]         =							None

				return min_value
			# No right subtree corner case
			# The structure of the tree implies that this should be the bottom root
			# and there is at least one other root
			if self.min_node.right is None:
				# Update size
				self.size -= 1

				# Update bottom root
				__snake_case      :		List[str]         =							self.bottom_root.parent
				__snake_case      :		int         =							None

				# Update min_node
				__snake_case      :		Union[str, Any]         =							self.bottom_root
				__snake_case      :		Any         =							self.bottom_root.parent
				while i:
					if i.val < self.min_node.val:
						__snake_case      :		Dict         =							i
					__snake_case      :		str         =							i.parent
				return min_value
			# General case
			# Find the BinomialHeap of the right subtree of min_node
			__snake_case      :		List[Any]         =							self.min_node.right
			__snake_case      :		str         =							None
			__snake_case      :		Tuple         =							bottom_of_new
			__snake_case      :		Optional[Any]         =							1

			# Size, min_node and bottom_root
			while bottom_of_new.left:
				__snake_case      :		str         =							size_of_new * 2 + 1
				__snake_case      :		Union[str, Any]         =							bottom_of_new.left
				if bottom_of_new.val < min_of_new.val:
					__snake_case      :		Dict         =							bottom_of_new
        # Corner case of single root on top left path
			if (not self.min_node.left) and (not self.min_node.parent):
				__snake_case      :		List[str]         =							size_of_new
				__snake_case      :		str         =							bottom_of_new
				__snake_case      :		Optional[Any]         =							min_of_new
				# print("Single root, multiple nodes case")
				return min_value
			# Remaining cases
			# Construct heap of right subtree
			__snake_case      :		Optional[int]         =							BinomialHeap(
			    bottom_root=a_							,			min_node=a_							,			heap_size=a_   )

			# Update size
			__snake_case      :		List[str]         =							self.size - 1 - size_of_new

			# Neighbour nodes
			__snake_case      :		Dict         =							self.min_node.left
			__snake_case      :		Dict         =							self.min_node.parent

			# Initialize new bottom_root and min_node
			__snake_case      :		List[Any]         =							previous_node or next_node
			__snake_case      :		Union[str, Any]         =							next_node

			# Update links of previous_node and search below for new min_node and
			# bottom_root
			if previous_node:
				__snake_case      :		Optional[int]         =							next_node

				# Update bottom_root and search for min_node below
				__snake_case      :		Optional[Any]         =							previous_node
				__snake_case      :		str         =							previous_node
				while self.bottom_root.left:
					__snake_case      :		Any         =							self.bottom_root.left
					if self.bottom_root.val < self.min_node.val:
						__snake_case      :		Tuple         =							self.bottom_root
			if next_node:
				__snake_case      :		Optional[int]         =							previous_node

				# Search for new min_node above min_node
				__snake_case      :		Tuple         =							next_node
				while i:
					if i.val < self.min_node.val:
						__snake_case      :		List[str]         =							i
					__snake_case      :		int         =							i.parent
        # Merge heaps
			self.merge_heaps(a_   )

			return min_value



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			__snake_case      :		Dict         =							self.bottom_root
			while top_root.parent:
				__snake_case      :		Optional[int]         =							top_root.parent
			# preorder
			__snake_case      :		Dict         =							[]
			self.__traversal(a_							,			a_   )
			return heap_pre_order



		def 							SCREAMING_SNAKE_CASE    (self							,			a_							,			a_							,			a_=0   ):





			'''simple docstring'''

			if curr_node:
				preorder.append((curr_node.val, level)   )
				self.__traversal(curr_node.left							,			a_							,			level + 1   )
				self.__traversal(curr_node.right							,			a_							,			level + 1   )
			else:
				preorder.append(('''#''', level)   )



		def __str__(self   ):





			'''simple docstring'''

			if self.is_empty():
				return ""
			__snake_case      :		List[Any]         =							self.pre_order()

			return "\n".join(('''-''' * level + str(a_   )) for value, level in preorder_heap   )


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

			doctest.testmod()










'''simple docstring'''

from __future__ import annotations

import sys







def     __UpperCamelCase					(				_lowercase       )			->      int:
	if n < 0:
		raise ValueError('Negative arguments are not supported'       )
	return _fib(_lowercase       )[0]







def     __UpperCamelCase					(				_lowercase       )			->      tuple[int, int]:
	if n == 0:  # (F(0), F(1))
		return (0, 1)

	# F(2n) = F(n)[2F(n+1) − F(n)]
	# F(2n+1) = F(n+1)^2+F(n)^2
	_lowercase	,     _lowercase       :							List[str]  	=		_fib(n // 2       )
	_lowercase       :							Dict  	=		a * (b * 2 - a)
	_lowercase       :							Union[str, Any]  	=		a * a + b * b
	return (d, c + d) if n % 2 else (c, d)


if __name__ == "__main__":
		_A					:     Optional[Any]      =int(sys.argv[1])
		print(F'''fibonacci({n}) is {fibonacci(n)}''')
