






def       _a   (							lowerCamelCase__				)  ->      int:
 if not isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  raise TypeError('recursive_lucas_number accepts only integer arguments.'				)
 if n_th_number == 0:
  return 2
 if n_th_number == 1:
  return 1

 return recursive_lucas_number(n_th_number - 1				) + recursive_lucas_number(
     n_th_number - 2				)




def       _a   (							lowerCamelCase__				)  ->      int:
 if not isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  raise TypeError('dynamic_lucas_number accepts only integer arguments.'				)
 lowerCamelCase_		,      lowerCamelCase_							:    Tuple							=     2, 1
 for _ in range(lowerCamelCase__				):
  lowerCamelCase_		,      lowerCamelCase_							:    Any							=     b, a + b
 return a


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       UpperCamelCase											=      int(input('''Enter the number of terms in lucas series:\n''').strip())
       print('''Using recursive function to calculate lucas series:''')
       print(''' '''.join(str(recursive_lucas_number(i)) for i in range(n)))
       print('''\nUsing dynamic function to calculate lucas series:''')
       print(''' '''.join(str(dynamic_lucas_number(i)) for i in range(n)))








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()
