


'''simple docstring'''


def        __lowerCAmelCase       (__lowerCAmelCase      ):

		if not isinstance(_lowercase					,       _lowercase      ):
				raise TypeError("only integers accepted as input"      )
		else:
				_UpperCAmelCase						:				str	    =					str(abs(_lowercase      )      )
				_UpperCAmelCase						:				str	    =					[list(_lowercase      ) for char in range(len(_lowercase      )      )]
				for index in range(len(_lowercase      )      ):
						num_transpositions[index].pop(_lowercase      )
				return max(
				    int("".join(list(_lowercase      )      )      ) for transposition in num_transpositions      )


if __name__ == "__main__":
						__import__('doctest').testmod()








'''simple docstring'''




from __future__ import annotations

import math

class 			UpperCamelCase_ :





	def __init__(  self		,		A    )			->			None:
								UpperCAmelCase     :		Optional[int]							     =		size
								# approximate the overall size of segment tree with given value
								UpperCAmelCase     :		Optional[int]							     =		[0 for i in range(0		,		4 * size    )]
								# create array to store lazy update
								UpperCAmelCase     :		Any							     =		[0 for i in range(0		,		4 * size    )]
								UpperCAmelCase     :		Tuple							     =		[0 for i in range(0		,		4 * size    )]  # flag for lazy update





	def  _lowercase(  self		,		A    )			->			int:
								return idx * 2





	def  _lowercase(  self		,		A    )			->			int:
								return idx * 2 + 1





	def  _lowercase(  self		,		A		,		A		,		A		,		A    )			->			None:
								if left_element == right_element:
															UpperCAmelCase     :		str							     =		a[left_element - 1]
								else:
															UpperCAmelCase     :		Tuple							     =		(left_element + right_element) // 2
															self.build(self.left(A    )		,		A		,		A		,		A    )
															self.build(self.right(A    )		,		mid + 1		,		A		,		A    )
															UpperCAmelCase     :		str							     =		max(
															    self.segment_tree[self.left(A    )]		,		self.segment_tree[self.right(A    )]    )





	def  _lowercase(  self		,		A		,		A		,		A		,		A		,		A		,		A    )			->			bool:
								if self.flag[idx] is True:
															UpperCAmelCase     :		Optional[Any]							     =		self.lazy[idx]
															UpperCAmelCase     :		int							     =		False
															if left_element != right_element:
																						UpperCAmelCase     :		List[str]							     =		self.lazy[idx]
																						UpperCAmelCase     :		Optional[Any]							     =		self.lazy[idx]
																						UpperCAmelCase     :		List[str]							     =		True
																						UpperCAmelCase     :		int							     =		True

								if right_element < a or left_element > b:
															return True
								if left_element >= a and right_element <= b:
															UpperCAmelCase     :		Optional[Any]							     =		val
															if left_element != right_element:
																						UpperCAmelCase     :		Tuple							     =		val
																						UpperCAmelCase     :		int							     =		val
																						UpperCAmelCase     :		Any							     =		True
																						UpperCAmelCase     :		str							     =		True
															return True
								UpperCAmelCase     :		str							     =		(left_element + right_element) // 2
								self.update(self.left(A    )		,		A		,		A		,		A		,		A		,		A    )
								self.update(self.right(A    )		,		mid + 1		,		A		,		A		,		A		,		A    )
								UpperCAmelCase     :		List[str]							     =		max(
								    self.segment_tree[self.left(A    )]		,		self.segment_tree[self.right(A    )]    )
								return True





	def  _lowercase(  self		,		A		,		A		,		A		,		A		,		A    )			->			int | float:
								if self.flag[idx] is True:
															UpperCAmelCase     :		Any							     =		self.lazy[idx]
															UpperCAmelCase     :		Any							     =		False
															if left_element != right_element:
																						UpperCAmelCase     :		Optional[Any]							     =		self.lazy[idx]
																						UpperCAmelCase     :		Tuple							     =		self.lazy[idx]
																						UpperCAmelCase     :		List[str]							     =		True
																						UpperCAmelCase     :		Tuple							     =		True
								if right_element < a or left_element > b:
															return -math.inf
								if left_element >= a and right_element <= b:
															return self.segment_tree[idx]
								UpperCAmelCase     :		Dict							     =		(left_element + right_element) // 2
								UpperCAmelCase     :		List[Any]							     =		self.query(self.left(A    )		,		A		,		A		,		A		,		A    )
								UpperCAmelCase     :		str							     =		self.query(self.right(A    )		,		mid + 1		,		A		,		A		,		A    )
								return max(A		,		A    )






	def __str__(  self    )			->			str:
								return str([self.query(1		,		1		,		self.size		,		A		,		A    ) for i in range(1		,		self.size + 1    )]    )


if __name__ == "__main__":
							a   :			Optional[int]					  =    [1, 2, -4, 7, 3, -5, 6, 1_1, -2_0, 9, 1_4, 1_5, 5, 2, -8]
							a   :			Optional[Any]					  =    1_5
							a   :			Union[str, Any]					  =    SegmentTree(size)
							segt.build(1, 1, size, A)
							print(segt.query(1, 1, size, 4, 6))
							print(segt.query(1, 1, size, 7, 1_1))
							print(segt.query(1, 1, size, 7, 1_2))
							segt.update(1, 1, size, 1, 3, 1_1_1)
							print(segt.query(1, 1, size, 1, 1_5))
							segt.update(1, 1, size, 7, 8, 2_3_5)
							print(segt)

