





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()







import numpy as np






def 				_lowerCAmelCase			(	_a :       Optional[int]       , _a :       str      )						->      Union[str, Any]:
     lowerCAmelCase_       :							int			 =		np.array(_a      )
     lowerCAmelCase_       :							str			 =		np.array(_a      )

     lowerCAmelCase_       :							Optional[Any]			 =		abs(predict - actual      )
     lowerCAmelCase_       :							Dict			 =		difference.mean()

     return score






def 				_lowerCAmelCase			(	_a :       Union[str, Any]       , _a :       int      )						->      Tuple:
     lowerCAmelCase_       :							int			 =		np.array(_a      )
     lowerCAmelCase_       :							int			 =		np.array(_a      )

     lowerCAmelCase_       :							Union[str, Any]			 =		predict - actual
     lowerCAmelCase_       :							Tuple			 =		np.square(_a      )

     lowerCAmelCase_       :							Tuple			 =		square_diff.mean()
     return score






def 				_lowerCAmelCase			(	_a :       Optional[Any]       , _a :       Tuple      )						->      Optional[int]:
     lowerCAmelCase_       :							Optional[Any]			 =		np.array(_a      )
     lowerCAmelCase_       :							Optional[Any]			 =		np.array(_a      )

     lowerCAmelCase_       :							int			 =		predict - actual
     lowerCAmelCase_       :							Any			 =		np.square(_a      )
     lowerCAmelCase_       :							Union[str, Any]			 =		square_diff.mean()
     lowerCAmelCase_       :							Optional[Any]			 =		np.sqrt(_a      )
     return score






def 				_lowerCAmelCase			(	_a :       Optional[Any]       , _a :       Optional[Any]      )						->      List[Any]:
     lowerCAmelCase_       :							Dict			 =		np.array(_a      )
     lowerCAmelCase_       :							List[Any]			 =		np.array(_a      )

     lowerCAmelCase_       :							str			 =		np.log(predict + 1      )
     lowerCAmelCase_       :							Any			 =		np.log(actual + 1      )

     lowerCAmelCase_       :							List[str]			 =		log_predict - log_actual
     lowerCAmelCase_       :							Dict			 =		np.square(_a      )
     lowerCAmelCase_       :							Optional[Any]			 =		square_diff.mean()

     lowerCAmelCase_       :							int			 =		np.sqrt(_a      )

     return score






def 				_lowerCAmelCase			(	_a :       str       , _a :       List[Any]      )						->      int:
     lowerCAmelCase_       :							Any			 =		np.array(_a      )
     lowerCAmelCase_       :							Optional[int]			 =		np.array(_a      )

     lowerCAmelCase_       :							Optional[int]			 =		predict - actual
     lowerCAmelCase_       :							str			 =		np.sum(_a      ) / len(_a      )
     lowerCAmelCase_       :							List[str]			 =		np.sum(_a      ) / len(_a      )
     # print(numerator, denumerator)
     lowerCAmelCase_       :							int			 =		float(_a      ) / denumerator * 1_00

     return score







def 				_lowerCAmelCase			(	_a :       Any       , _a :       Union[str, Any]      )						->      str:
     return np.mean(np.array(_a      ) == np.array(_a      )      )
