





import itertools






def 				_lowerCAmelCase			(	_a :       int = 1_00_00_00      )						->      int:
     lowerCAmelCase_       :							Optional[Any]			 =		[1]

     for i in itertools.count(len(_a      )      ):
          lowerCAmelCase_       :							str			 =		0
          for j in itertools.count(1      ):
               lowerCAmelCase_       :							int			 =		-1 if j % 2 == 0 else +1
               lowerCAmelCase_       :							Dict			 =		(j * j * 3 - j) // 2
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number
               index += j
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number

          if item == 0:
               return i
          partitions.append(_a      )

     return 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      print(F"""{solution() = }""")







import math





class   lowercase__     :







  def __init__(						self     ,    _lowercase    ):
       lowerCAmelCase_       :							Optional[Any]			 =		len(_lowercase    )
       lowerCAmelCase_       :							Union[str, Any]			 =		[0] * (
           4 * self.N
       )  # approximate the overall size of segment tree with array N
       self.build(1     ,    0     ,    self.N - 1    )







  def 						UpperCAmelCase__		(						self     ,    _lowercase    ):
       return idx * 2







  def 						UpperCAmelCase__		(						self     ,    _lowercase    ):
       return idx * 2 + 1







  def 						UpperCAmelCase__		(						self     ,    _lowercase     ,    _lowercase     ,    _lowercase    ):  # noqa: E741
       if l == r:
            lowerCAmelCase_       :							Dict			 =		A[l]
       else:
            lowerCAmelCase_       :							List[str]			 =		(l + r) // 2
            self.build(self.left(_lowercase    )     ,    _lowercase     ,    _lowercase    )
            self.build(self.right(_lowercase    )     ,    mid + 1     ,    _lowercase    )
            lowerCAmelCase_       :							Dict			 =		max(self.st[self.left(_lowercase    )]     ,    self.st[self.right(_lowercase    )]    )







  def 						UpperCAmelCase__		(						self     ,    _lowercase     ,    _lowercase     ,    _lowercase    ):
       return self.update_recursive(1     ,    0     ,    self.N - 1     ,    a - 1     ,    b - 1     ,    _lowercase    )







  def 						UpperCAmelCase__		(						self     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase    ):  # noqa: E741
       if r < a or l > b:
            return True
       if l == r:
            lowerCAmelCase_       :							List[str]			 =		val
            return True
       lowerCAmelCase_       :							List[str]			 =		(l + r) // 2
       self.update_recursive(self.left(_lowercase    )     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase    )
       self.update_recursive(self.right(_lowercase    )     ,    mid + 1     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase    )
       lowerCAmelCase_       :							List[Any]			 =		max(self.st[self.left(_lowercase    )]     ,    self.st[self.right(_lowercase    )]    )
       return True







  def 						UpperCAmelCase__		(						self     ,    _lowercase     ,    _lowercase    ):
       return self.query_recursive(1     ,    0     ,    self.N - 1     ,    a - 1     ,    b - 1    )







  def 						UpperCAmelCase__		(						self     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase    ):  # noqa: E741
       if r < a or l > b:
            return -math.inf
       if l >= a and r <= b:
            return self.st[idx]
       lowerCAmelCase_       :							int			 =		(l + r) // 2
       lowerCAmelCase_       :							List[Any]			 =		self.query_recursive(self.left(_lowercase    )     ,    _lowercase     ,    _lowercase     ,    _lowercase     ,    _lowercase    )
       lowerCAmelCase_       :							List[str]			 =		self.query_recursive(self.right(_lowercase    )     ,    mid + 1     ,    _lowercase     ,    _lowercase     ,    _lowercase    )
       return max(_lowercase     ,    _lowercase    )







  def 						UpperCAmelCase__		(						self    ):
       lowerCAmelCase_       :							List[Any]			 =		[]
       for i in range(1     ,    N + 1    ):
            show_list += [self.query(_lowercase     ,    _lowercase    )]
       print(_lowercase    )


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