





"""simple docstring"""




def 						UpperCAmelCase__		(     _UpperCAmelCase ,					_UpperCAmelCase					):






  """simple docstring"""





  assert x is not None
  assert y is not None

  A_  :       int										=  len(_UpperCAmelCase					)
  A_  :       List[Any]										=  len(_UpperCAmelCase					)

  # declaring the array for storing the dp values
  A_  :       int										=  [[0] * (n + 1) for _ in range(m + 1					)]  # noqa: E741

  for i in range(1 ,					m + 1					):
    for j in range(1 ,					n + 1					):
      A_  :       List[Any]										=  1 if x[i - 1] == y[j - 1] else 0

      A_  :       Dict										=  max(l[i - 1][j] ,					l[i][j - 1] ,					l[i - 1][j - 1] + match					)

  A_  :       str										=  ''
  A_						,       A_  :       Any										=  m, n
  while i > 0 and j > 0:
    A_  :       Union[str, Any]										=  1 if x[i - 1] == y[j - 1] else 0

    if l[i][j] == l[i - 1][j - 1] + match:
      if match == 1:
        A_  :       Union[str, Any]										=  x[i - 1] + seq
      i -= 1
      j -= 1
    elif l[i][j] == l[i - 1][j]:
      i -= 1
    else:
      j -= 1

  return l[m][n], seq


if __name__ == "__main__":
   lowerCamelCase_     :						str						=					'AGGTAB'
   lowerCamelCase_     :						str						=					'GXTXAYB'
   lowerCamelCase_     :						List[str]						=					4
   lowerCamelCase_     :						Tuple						=					'GTAB'

   lowerCamelCase_					,					lowerCamelCase_     :						List[str]						=					longest_common_subsequence(a, b)
   print('len =', ln, ', sub-sequence =', subseq)
   import doctest

   doctest.testmod()






"""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()