def 					SCREAMING_SNAKE_CASE_			(		lowerCAmelCase_: list[int]     ):
      if len(lowerCAmelCase_     ) > 1:
            snake_case_     :			List[str]       =       len(lowerCAmelCase_     ) // 2  # Finds the middle of the array
            snake_case_     :			Tuple       =       arr[
                :middle_length
            ]  # Creates an array of the elements in the first half.
            snake_case_     :			Any       =       arr[
                middle_length:
            ]  # Creates an array of the elements in the second half.
            snake_case_     :			List[Any]       =       len(lowerCAmelCase_     )
            snake_case_     :			Optional[int]       =       len(lowerCAmelCase_     )
            merge(lowerCAmelCase_     )  # Starts sorting the left.
            merge(lowerCAmelCase_     )  # Starts sorting the right
            snake_case_     :			List[Any]       =       0  # Left Counter
            snake_case_     :			Any       =       0  # Right Counter
            snake_case_     :			Optional[Any]       =       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]:
                        snake_case_     :			List[str]       =       left_array[left_index]
                        left_index += 1
                  else:
                        snake_case_     :			List[str]       =       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
                  snake_case_     :			List[str]       =       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
                  snake_case_     :			Tuple       =       right_array[right_index]
                  right_index += 1
                  index += 1
      return arr


if __name__ == "__main__":
     import doctest

     doctest.testmod()




import math



class 					snake_case__       :



   def __init__(				self   :   int			,	A__   :   str   )							->     int:




         '''simple docstring'''




         snake_case_     :			Tuple       =       len(A__   )
         snake_case_     :			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   :   Optional[Any]			,	A__   :   Tuple   )							->     Optional[int]:




         '''simple docstring'''




         return idx * 2



   def 					UpperCAmelCase__       (				self   :   Union[str, Any]			,	A__   :   List[str]   )							->     Dict:




         '''simple docstring'''




         return idx * 2 + 1



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




         '''simple docstring'''




         if l == r:
               snake_case_     :			str       =       A[l]
         else:
               snake_case_     :			List[str]       =       (l + r) // 2
               self.build(self.left(A__   )			,	A__			,	A__   )
               self.build(self.right(A__   )			,	mid + 1			,	A__   )
               snake_case_     :			Union[str, Any]       =       max(self.st[self.left(A__   )]			,	self.st[self.right(A__   )]   )



   def 					UpperCAmelCase__       (				self   :   Optional[Any]			,	A__   :   List[str]			,	A__   :   Union[str, Any]			,	A__   :   str   )							->     int:




         '''simple docstring'''




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



   def 					UpperCAmelCase__       (				self   :   Optional[int]			,	A__   :   Optional[Any]			,	A__   :   List[str]			,	A__   :   Optional[Any]			,	A__   :   Union[str, Any]			,	A__   :   List[Any]			,	A__   :   str   )							->     Any:  # noqa: E741




         '''simple docstring'''




         if r < a or l > b:
               return True
         if l == r:
               snake_case_     :			List[str]       =       val
               return True
         snake_case_     :			Dict       =       (l + r) // 2
         self.update_recursive(self.left(A__   )			,	A__			,	A__			,	A__			,	A__			,	A__   )
         self.update_recursive(self.right(A__   )			,	mid + 1			,	A__			,	A__			,	A__			,	A__   )
         snake_case_     :			Tuple       =       max(self.st[self.left(A__   )]			,	self.st[self.right(A__   )]   )
         return True



   def 					UpperCAmelCase__       (				self   :   Optional[int]			,	A__   :   List[Any]			,	A__   :   Optional[Any]   )							->     str:




         '''simple docstring'''




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



   def 					UpperCAmelCase__       (				self   :   Union[str, Any]			,	A__   :   Any			,	A__   :   int			,	A__   :   Tuple			,	A__   :   Tuple			,	A__   :   Dict   )							->     str:  # noqa: E741




         '''simple docstring'''




         if r < a or l > b:
               return -math.inf
         if l >= a and r <= b:
               return self.st[idx]
         snake_case_     :			Dict       =       (l + r) // 2
         snake_case_     :			Optional[Any]       =       self.query_recursive(self.left(A__   )			,	A__			,	A__			,	A__			,	A__   )
         snake_case_     :			Any       =       self.query_recursive(self.right(A__   )			,	mid + 1			,	A__			,	A__			,	A__   )
         return max(A__			,	A__   )



   def 					UpperCAmelCase__       (				self   :   Dict   )							->     Optional[Any]:




         '''simple docstring'''




         snake_case_     :			int       =       []
         for i in range(1			,	N + 1   ):
               show_list += [self.query(A__			,	A__   )]
         print(A__   )


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()



