




def 	lowerCAmelCase_	(     lowerCamelCase:				list[int]  )    ->	tuple[int, int]:


      '''simple docstring'''




      if len(lowerCamelCase  ) == 1:
            return a[0], a[0]
      else:
            # split A into half.
            lowerCamelCase__					     = a[: len(lowerCamelCase  ) // 2]
            lowerCamelCase__					     = a[len(lowerCamelCase  ) // 2 :]

            # 2 sub problems, 1/2 of original size.
            lowerCamelCase__     ,						lowerCamelCase__					     = max_difference(lowerCamelCase  )
            lowerCamelCase__     ,						lowerCamelCase__					     = max_difference(lowerCamelCase  )

            # get min of first and max of second
            # linear time
            lowerCamelCase__					     = min(lowerCamelCase  )
            lowerCamelCase__					     = max(lowerCamelCase  )

            # 3 cases, either (small1, big1),
            # (min_first, max_second), (small2, big2)
            # constant comparisons
            if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
                  return smalla, biga
            elif biga - smalla > max_second - min_first:
                  return smalla, biga
            else:
                  return min_first, max_second


if __name__ == "__main__":
      import doctest

      doctest.testmod()





def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	int:


      '''simple docstring'''




      return n * (2 * n - 1)

def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	bool:


      '''simple docstring'''




      lowerCamelCase__					     = (1 + 24 * n) ** 0.5
      return ((1 + root) / 6) % 1 == 0

def 	lowerCAmelCase_	(     lowerCamelCase:				int = 1_44  )    ->	int:


      '''simple docstring'''




      lowerCamelCase__					     = start
      lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      while not is_pentagonal(lowerCamelCase  ):
            n += 1
            lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      return num


if __name__ == "__main__":
      print(F"""{solution()} = """)