
"""simple docstring"""




def 						__magic_name__		(				UpperCamelCase    :		int    )    ->	int:

    if not isinstance(UpperCamelCase       ,		UpperCamelCase    ) or number < 0:
        raise ValueError('Input must be a non-negative integer'    )

    a__    = number & ~(number - 1)
    a__    = 0
    while intermediate:
        intermediate >>= 1
        index += 1
    return index - 1


if __name__ == "__main__":
    import doctest

    doctest.testmod(verbose=True)




"""simple docstring"""




import math







class 						lowercase:



     def __init__(       self    ,							__SCREAMING_SNAKE_CASE      )		->    Optional[int]:







         """simple docstring"""



         a__    = len(__SCREAMING_SNAKE_CASE      )
         a__    = [0] * (
             4 * self.N
         )  # approximate the overall size of segment tree with array N
         self.build(1    ,							0    ,							self.N - 1      )



     def  lowercase__     (       self    ,							__SCREAMING_SNAKE_CASE      )		->    Optional[Any]:







         """simple docstring"""



         return idx * 2



     def  lowercase__     (       self    ,							__SCREAMING_SNAKE_CASE      )		->    Optional[int]:







         """simple docstring"""



         return idx * 2 + 1



     def  lowercase__     (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )		->    List[str]:  # noqa: E741







         """simple docstring"""



         if l == r:
             a__    = A[l]
         else:
             a__    = (l + r) // 2
             self.build(self.left(__SCREAMING_SNAKE_CASE      )    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )
             self.build(self.right(__SCREAMING_SNAKE_CASE      )    ,							mid + 1    ,							__SCREAMING_SNAKE_CASE      )
             a__    = max(self.st[self.left(__SCREAMING_SNAKE_CASE      )]    ,							self.st[self.right(__SCREAMING_SNAKE_CASE      )]      )



     def  lowercase__     (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )		->    int:







         """simple docstring"""



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



     def  lowercase__     (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )		->    Optional[int]:  # noqa: E741







         """simple docstring"""



         if r < a or l > b:
             return True
         if l == r:
             a__    = val
             return True
         a__    = (l + r) // 2
         self.update_recursive(self.left(__SCREAMING_SNAKE_CASE      )    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )
         self.update_recursive(self.right(__SCREAMING_SNAKE_CASE      )    ,							mid + 1    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )
         a__    = max(self.st[self.left(__SCREAMING_SNAKE_CASE      )]    ,							self.st[self.right(__SCREAMING_SNAKE_CASE      )]      )
         return True



     def  lowercase__     (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )		->    List[str]:







         """simple docstring"""



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



     def  lowercase__     (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )		->    Any:  # noqa: E741







         """simple docstring"""



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




     def  lowercase__     (       self      )		->    List[Any]:







         """simple docstring"""



         a__    = []
         for i in range(1    ,							N + 1      ):
             show_list += [self.query(__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE      )]
         print(__SCREAMING_SNAKE_CASE      )


if __name__ == "__main__":
    a		:					Union[str, Any]    	=					[1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
    a		:					Dict    	=					15
    a		:					Tuple    	=					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()


