






import math




class 	lowerCamelCase__				:






      def __init__(self					:    int		,		_snake_case					:    Dict		)       ->   Union[str, Any]:


       """simple docstring"""






       lowerCamelCase_							:    Optional[Any]							=     len(_snake_case		)
       lowerCamelCase_							:    Optional[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					:    List[str]		,		_snake_case					:    List[str]		)       ->   int:


       """simple docstring"""






       return idx * 2






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    Dict		)       ->   Optional[Any]:


       """simple docstring"""






       return idx * 2 + 1






      def      UpperCAmelCase_     (self					:    List[Any]		,		_snake_case					:    List[Any]		,		_snake_case					:    str		,		_snake_case					:    List[Any]		)       ->   Optional[Any]:  # noqa: E741


       """simple docstring"""






       if l == r:
        lowerCamelCase_							:    List[Any]							=     A[l]
       else:
        lowerCamelCase_							:    int							=     (l + r) // 2
        self.build(self.left(_snake_case		)		,		_snake_case		,		_snake_case		)
        self.build(self.right(_snake_case		)		,		mid + 1		,		_snake_case		)
        lowerCamelCase_							:    Tuple							=     max(self.st[self.left(_snake_case		)]		,		self.st[self.right(_snake_case		)]		)






      def      UpperCAmelCase_     (self					:    str		,		_snake_case					:    Tuple		,		_snake_case					:    Any		,		_snake_case					:    str		)       ->   Tuple:


       """simple docstring"""






       return self.update_recursive(1		,		0		,		self.N - 1		,		a - 1		,		b - 1		,		_snake_case		)






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    List[str]		,		_snake_case					:    Tuple		,		_snake_case					:    Optional[int]		,		_snake_case					:    int		,		_snake_case					:    Tuple		,		_snake_case					:    List[str]		)       ->   Optional[Any]:  # noqa: E741


       """simple docstring"""






       if r < a or l > b:
        return True
       if l == r:
        lowerCamelCase_							:    Tuple							=     val
        return True
       lowerCamelCase_							:    Optional[int]							=     (l + r) // 2
       self.update_recursive(self.left(_snake_case		)		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       self.update_recursive(self.right(_snake_case		)		,		mid + 1		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       lowerCamelCase_							:    Union[str, Any]							=     max(self.st[self.left(_snake_case		)]		,		self.st[self.right(_snake_case		)]		)
       return True






      def      UpperCAmelCase_     (self					:    List[Any]		,		_snake_case					:    List[Any]		,		_snake_case					:    Optional[int]		)       ->   str:


       """simple docstring"""






       return self.query_recursive(1		,		0		,		self.N - 1		,		a - 1		,		b - 1		)






      def      UpperCAmelCase_     (self					:    Any		,		_snake_case					:    List[Any]		,		_snake_case					:    Optional[Any]		,		_snake_case					:    int		,		_snake_case					:    Optional[int]		,		_snake_case					:    Optional[Any]		)       ->   str:  # noqa: E741


       """simple docstring"""






       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_							:    Optional[Any]							=     self.query_recursive(self.left(_snake_case		)		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       lowerCamelCase_							:    Union[str, Any]							=     self.query_recursive(self.right(_snake_case		)		,		mid + 1		,		_snake_case		,		_snake_case		,		_snake_case		)
       return max(_snake_case		,		_snake_case		)






      def      UpperCAmelCase_     (self					:    str		)       ->   Tuple:


       """simple docstring"""






       lowerCamelCase_							:    Dict							=     []
       for i in range(1		,		N + 1		):
        show_list += [self.query(_snake_case		,		_snake_case		)]
       print(_snake_case		)


if __name__ == "__main__":
       UpperCamelCase											=      [1, 2, -4, 7, 3, -5, 6, 1_1, -2_0, 9, 1_4, 1_5, 5, 2, -8]
       UpperCamelCase											=      1_5
       UpperCamelCase											=      SegmentTree(A)
       print(segt.query(4, 6))
       print(segt.query(7, 1_1))
       print(segt.query(7, 1_2))
       segt.update(1, 3, 1_1_1)
       print(segt.query(1, 1_5))
       segt.update(7, 8, 2_3_5)
       segt.show_data()








def       _a   (							lowerCamelCase__				)  ->      list[int]:
 if len(lowerCamelCase__				) > 1:
  lowerCamelCase_							:    Optional[Any]							=     len(lowerCamelCase__				) // 2  # Finds the middle of the array
  lowerCamelCase_							:    int							=     arr[
      :middle_length
  ]  # Creates an array of the elements in the first half.
  lowerCamelCase_							:    List[Any]							=     arr[
      middle_length:
  ]  # Creates an array of the elements in the second half.
  lowerCamelCase_							:    Optional[Any]							=     len(lowerCamelCase__				)
  lowerCamelCase_							:    Optional[Any]							=     len(lowerCamelCase__				)
  merge(lowerCamelCase__				)  # Starts sorting the left.
  merge(lowerCamelCase__				)  # Starts sorting the right
  lowerCamelCase_							:    Dict							=     0  # Left Counter
  lowerCamelCase_							:    str							=     0  # Right Counter
  lowerCamelCase_							:    Tuple							=     0  # Position Counter
  while (
      left_index < left_size and right_index < right_size
  ):  # Runs until the lowers size of the left and right are sorted.
   if left_array[left_index] < right_array[right_index]:
    lowerCamelCase_							:    Optional[int]							=     left_array[left_index]
    left_index += 1
   else:
    lowerCamelCase_							:    Union[str, Any]							=     right_array[right_index]
    right_index += 1
   index += 1
  while (
      left_index < left_size
  ):  # Adds the left over elements in the left half of the array
   lowerCamelCase_							:    Tuple							=     left_array[left_index]
   left_index += 1
   index += 1
  while (
      right_index < right_size
  ):  # Adds the left over elements in the right half of the array
   lowerCamelCase_							:    Optional[int]							=     right_array[right_index]
   right_index += 1
   index += 1
 return arr


if __name__ == "__main__":
       import doctest

       doctest.testmod()
