





"""simple docstring"""




from __future__ import annotations





def 						UpperCAmelCase__		(     _UpperCAmelCase					):






  """simple docstring"""





  A_  :       List[str]										=  str(_UpperCAmelCase					)
  return len(_UpperCAmelCase					) == 9 and set(_UpperCAmelCase					) == set('123456789'					)





def 						UpperCAmelCase__		(     ):






  """simple docstring"""





  for base_num in range(9999 ,					4999 ,					-1					):
    A_  :       Union[str, Any]										=  100002 * base_num
    if is_9_pandigital(_UpperCAmelCase					):
      return candidate

  for base_num in range(333 ,					99 ,					-1					):
    A_  :       List[Any]										=  1002003 * base_num
    if is_9_pandigital(_UpperCAmelCase					):
      return candidate

  return None


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






"""simple docstring"""




from copy import deepcopy

class  _UpperCAmelCase  :



      '''simple docstring'''

      def __init__(     self					,      snake_case_ = None					,      snake_case_ = None  ):

        """simple docstring"""

        if arr is None and size is not None:
          A_  :       Union[str, Any]										=  size
          A_  :       List[str]										=  [0] * size
        elif arr is not None:
          self.init(snake_case_  )
        else:
          raise ValueError('Either arr or size must be specified'  )

      def 					lowerCamelCase_			(     self					,      snake_case_  ):

        """simple docstring"""

        A_  :       Union[str, Any]										=  len(snake_case_  )
        A_  :       Optional[int]										=  deepcopy(snake_case_  )
        for i in range(1					,      self.size  ):
          A_  :       Optional[Any]										=  self.next_(snake_case_  )
          if j < self.size:
            self.tree[j] += self.tree[i]

      def 					lowerCamelCase_			(     self  ):

        """simple docstring"""

        A_  :       int										=  self.tree[:]
        for i in range(self.size - 1					,      0					,      -1  ):
          A_  :       Optional[int]										=  self.next_(snake_case_  )
          if j < self.size:
            arr[j] -= arr[i]
        return arr

      @staticmethod
      def 					lowerCamelCase_			(     snake_case_  ):

        """simple docstring"""

        return index + (index & (-index))

      @staticmethod
      def 					lowerCamelCase_			(     snake_case_  ):

        """simple docstring"""

        return index - (index & (-index))

      def 					lowerCamelCase_			(     self					,      snake_case_					,      snake_case_  ):

        """simple docstring"""

        if index == 0:
          self.tree[0] += value
          return
        while index < self.size:
          self.tree[index] += value
          A_  :       List[str]										=  self.next_(snake_case_  )

      def 					lowerCamelCase_			(     self					,      snake_case_					,      snake_case_  ):

        """simple docstring"""

        self.add(snake_case_					,      value - self.get(snake_case_  )  )

      def 					lowerCamelCase_			(     self					,      snake_case_  ):

        """simple docstring"""

        if right == 0:
          return 0
        A_  :       Any										=  self.tree[0]
        right -= 1  # make right inclusive
        while right > 0:
          result += self.tree[right]
          A_  :       Tuple										=  self.prev(snake_case_  )
        return result

      def 					lowerCamelCase_			(     self					,      snake_case_					,      snake_case_  ):

        """simple docstring"""

        return self.prefix(snake_case_  ) - self.prefix(snake_case_  )

      def 					lowerCamelCase_			(     self					,      snake_case_  ):

        """simple docstring"""

        return self.query(snake_case_					,      index + 1  )

      def 					lowerCamelCase_			(     self					,      snake_case_  ):

        """simple docstring"""

        value -= self.tree[0]
        if value < 0:
          return -1

        A_  :       List[Any]										=  1  # Largest power of 2 <= size
        while j * 2 < self.size:
          j *= 2

        A_  :       Tuple										=  0

        while j > 0:
          if i + j < self.size and self.tree[i + j] <= value:
            value -= self.tree[i + j]
            i += j
          j //= 2
        return i


if __name__ == "__main__":
   import doctest

   doctest.testmod()