





'''simple docstring'''




from __future__ import annotations

import math


class 					SCREAMING_SNAKE_CASE       :


     def __init__(		self		,      _UpperCAmelCase):

          '''simple docstring'''






          __A		:					int						=			size
          # approximate the overall size of segment tree with given value
          __A		:					Optional[Any]						=			[0 for i in range(0		,      4 * size)]
          # create array to store lazy update
          __A		:					Optional[Any]						=			[0 for i in range(0		,      4 * size)]
          __A		:					str						=			[0 for i in range(0		,      4 * size)]  # flag for lazy update


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          return idx * 2


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          return idx * 2 + 1


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          if left_element == right_element:
               __A		:					List[Any]						=			a[left_element - 1]
          else:
               __A		:					List[str]						=			(left_element + right_element) // 2
               self.build(self.left(_UpperCAmelCase)		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
               self.build(self.right(_UpperCAmelCase)		,      mid + 1		,      _UpperCAmelCase		,      _UpperCAmelCase)
               __A		:					Any						=			max(
                   self.segment_tree[self.left(_UpperCAmelCase)]		,      self.segment_tree[self.right(_UpperCAmelCase)])


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          if self.flag[idx] is True:
               __A		:					Optional[Any]						=			self.lazy[idx]
               __A		:					Optional[Any]						=			False
               if left_element != right_element:
                    __A		:					List[Any]						=			self.lazy[idx]
                    __A		:					Dict						=			self.lazy[idx]
                    __A		:					Tuple						=			True
                    __A		:					Union[str, Any]						=			True

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


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          if self.flag[idx] is True:
               __A		:					Union[str, Any]						=			self.lazy[idx]
               __A		:					List[str]						=			False
               if left_element != right_element:
                    __A		:					Union[str, Any]						=			self.lazy[idx]
                    __A		:					Optional[int]						=			self.lazy[idx]
                    __A		:					str						=			True
                    __A		:					Union[str, Any]						=			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]
          __A		:					Any						=			(left_element + right_element) // 2
          __A		:					int						=			self.query(self.left(_UpperCAmelCase)		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
          __A		:					Union[str, Any]						=			self.query(self.right(_UpperCAmelCase)		,      mid + 1		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
          return max(_UpperCAmelCase		,      _UpperCAmelCase)


     def __str__(		self):

          '''simple docstring'''






          return str([self.query(1		,      1		,      self.size		,      _UpperCAmelCase		,      _UpperCAmelCase) for i in range(1		,      self.size + 1)])


if __name__ == "__main__":
  lowercase__       : Union[str, Any]         =       [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
  lowercase__       : str         =       15
  lowercase__       : List[Any]         =       SegmentTree(size)
  segt.build(1, 1, size, A)
  print(segt.query(1, 1, size, 4, 6))
  print(segt.query(1, 1, size, 7, 11))
  print(segt.query(1, 1, size, 7, 12))
  segt.update(1, 1, size, 1, 3, 1_11)
  print(segt.query(1, 1, size, 1, 15))
  segt.update(1, 1, size, 7, 8, 2_35)
  print(segt)




'''simple docstring'''

from abc import ABC, abstractmethod
from argparse import ArgumentParser

class       __magic_name__		(       _UpperCamelCase  ):







							@staticmethod
							@abstractmethod
							def 				__lowercase     (				_UpperCAmelCase   :			ArgumentParser						):
									raise NotImplementedError()







							@abstractmethod
							def 				__lowercase     (				self   :			str						):
									raise NotImplementedError()




