





def     lowercase__       (       __lowercase						:  Optional[Any]					)			->				Tuple:



       """simple docstring"""






       if not isinstance(A_    ,  A_					):
              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     lowercase__       (       __lowercase						:  List[Any]					)			->				Tuple:



       """simple docstring"""






       if not isinstance(A_    ,  A_					):
              raise TypeError('dynamic_lucas_number accepts only integer arguments.'					)
       __UpperCamelCase	,						__UpperCamelCase	=  2, 1
       for _ in range(A_					):
              __UpperCamelCase	,						__UpperCamelCase	=  b, a + b
       return a


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

    testmod()
    a__							:							Any			=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)))







'''simple docstring'''
def     lowercase__       (       __lowercase						:  list    ,  __lowercase						:  int    ,  __lowercase						:  int    ,  __lowercase						:  int					)			->				int:



       """simple docstring"""






       __UpperCamelCase	=  int((lower_bound + upper_bound) // 2					)
       if array[r] == value:
              return r
       if lower_bound >= upper_bound:
              return -1
       if array[r] < value:
              return binary_search(__lowercase    ,  r + 1    ,  __lowercase    ,  __lowercase					)
       else:
              return binary_search(__lowercase    ,  __lowercase    ,  r - 1    ,  __lowercase					)
def     lowercase__       (       __lowercase						:  int    ,  __lowercase						:  list					)			->				list:



       """simple docstring"""






       __UpperCamelCase	=  0
       if matrix[index][0] == value:
              return [index, 0]
       while index < len(__lowercase					) and matrix[index][0] < value:
              __UpperCamelCase	=  binary_search(matrix[index]    ,  0    ,  len(matrix[index]					) - 1    ,  __lowercase					)
              if r != -1:
                     return [index, r]
              index += 1
       return [-1, -1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
