
"""simple docstring"""


from collections.abc import Sequence
from queue import Queue







class  lowerCAmelCase_ :



						'''simple docstring'''


						def __init__(       self   :					List[str]     ,A_   :					Any     ,A_   :					List[Any]     ,A_   :					str     ,A_   :					Optional[Any]=None     ,A_   :					List[Any]=None					)   ->      Optional[int]:
							A        =      start
							A        =      end
							A        =      val
							A        =      (start + end) // 2
							A        =      left
							A        =      right




						def __repr__(       self   :					List[str]					)   ->      Optional[Any]:
							return F'SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})'







class  lowerCAmelCase_ :



						'''simple docstring'''


						def __init__(       self   :					str     ,A_   :					Sequence     ,A_   :					Optional[Any]					)   ->      Dict:
							A        =      collection
							A        =      function
							if self.collection:
								A        =      self._build_tree(0     ,len(A_					) - 1					)


						def   _SCREAMING_SNAKE_CASE					(       self   :					Tuple     ,A_   :					Optional[int]     ,A_   :					Dict					)   ->      Dict:
							self._update_tree(self.root     ,A_     ,A_					)


						def   _SCREAMING_SNAKE_CASE					(       self   :					Dict     ,A_   :					int     ,A_   :					int					)   ->      Union[str, Any]:
							return self._query_range(self.root     ,A_     ,A_					)


						def   _SCREAMING_SNAKE_CASE					(       self   :					Any     ,A_   :					str     ,A_   :					Optional[int]					)   ->      Tuple:
							if start == end:
								return SegmentTreeNode(A_     ,A_     ,self.collection[start]					)
							A        =      (start + end) // 2
							A        =      self._build_tree(A_     ,A_					)
							A        =      self._build_tree(mid + 1     ,A_					)
							return SegmentTreeNode(A_     ,A_     ,self.fn(left.val     ,right.val					)     ,A_     ,A_					)


						def   _SCREAMING_SNAKE_CASE					(       self   :					List[str]     ,A_   :					List[Any]     ,A_   :					Union[str, Any]     ,A_   :					Any					)   ->      List[Any]:
							if node.start == i and node.end == i:
								A        =      val
								return
							if i <= node.mid:
								self._update_tree(node.left     ,A_     ,A_					)
							else:
								self._update_tree(node.right     ,A_     ,A_					)
							A        =      self.fn(node.left.val     ,node.right.val					)


						def   _SCREAMING_SNAKE_CASE					(       self   :					Tuple     ,A_   :					Dict     ,A_   :					List[str]     ,A_   :					Tuple					)   ->      str:
							if node.start == i and node.end == j:
								return node.val

							if i <= node.mid:
								if j <= node.mid:
									# range in left child tree
									return self._query_range(node.left     ,A_     ,A_					)
								else:
									# range in left child tree and right child tree
									return self.fn(
									    self._query_range(node.left     ,A_     ,node.mid					)     ,self._query_range(node.right     ,node.mid + 1     ,A_					)     ,)
							else:
								# range in right child tree
								return self._query_range(node.right     ,A_     ,A_					)




						def   _SCREAMING_SNAKE_CASE					(       self   :					Any					)   ->      List[str]:
							if self.root is not None:
								A        =      Queue()
								queue.put(self.root					)
								while not queue.empty():
									A        =      queue.get()
									yield node

									if node.left is not None:
										queue.put(node.left					)

									if node.right is not None:
										queue.put(node.right					)


if __name__ == "__main__":
		import operator

		for fn in [operator.add, max, min]:
				print('''*''' * 50)
				_lowercase							      = SegmentTree([2, 1, 5, 3, 4], fn)
				for node in arr.traverse():
						print(node)
				print()

				arr.update(1, 5)
				for node in arr.traverse():
						print(node)
				print()

				print(arr.query_range(3, 4))  # 7
				print(arr.query_range(2, 2))  # 5
				print(arr.query_range(1, 3))  # 13
				print()







from __future__ import annotations





def 						__UpperCAmelCase			(     a_							,     a_							,     a_							,     a_):  # noqa: E741
							while r - l > 1:
														snake_case_				=							(l + r) // 2
														if v[m] >= key:
																					snake_case_				=							m
														else:
																					snake_case_				=							m  # noqa: E741
							return r





def 						__UpperCAmelCase			(     a_):
							if len(a_) == 0:
														return 0

							snake_case_				=							[0] * len(a_)
							snake_case_				=							1

							snake_case_				=							v[0]

							for i in range(1							,     len(a_)):
														if v[i] < tail[0]:
																					snake_case_				=							v[i]
														elif v[i] > tail[length - 1]:
																					snake_case_				=							v[i]
																					length += 1
														else:
																					snake_case_				=							v[i]

							return length


if __name__ == "__main__":
	import doctest

	doctest.testmod()





