





def 							_lowerCAmelCase (  _a   :					list			)	->			int:

     if not grid or not grid[0]:
          raise TypeError("""The grid does not contain the appropriate information"""			)

     for cell_n in range(1					,   len(grid[0]			)			):
          grid[0][cell_n] += grid[0][cell_n - 1]
     lowerCAmelCase_					:       Tuple    =		grid[0]

     for row_n in range(1					,   len(_a			)			):
          lowerCAmelCase_					:       Any    =		grid[row_n]
          lowerCAmelCase_					:       Optional[Any]    =		fill_row(_a					,   _a			)
          lowerCAmelCase_					:       List[Any]    =		grid[row_n]

     return grid[-1][-1]






def 							_lowerCAmelCase (  _a   :					list					,   _a   :					list			)	->			list:
     current_row[0] += row_above[0]
     for cell_n in range(1					,   len(_a			)			):
          current_row[cell_n] += min(current_row[cell_n - 1]					,   row_above[cell_n]			)

     return current_row


if __name__ == "__main__":
      import doctest

      doctest.testmod()







from __future__ import annotations






def 							_lowerCAmelCase (  _a   :					list[int]			)	->			list[int]:  # This function is recursive
     lowerCAmelCase_					:       List[Any]    =		len(_a			)
     # If the array contains only one element, we return it (it's the stop condition of
     # recursion)
     if array_length <= 1:
          return array
          # Else
     lowerCAmelCase_					:       Union[str, Any]    =		array[0]
     lowerCAmelCase_					:       str    =		False
     lowerCAmelCase_					:       Optional[int]    =		1
     lowerCAmelCase_					:       list[int]    =		[]
     while not is_found and i < array_length:
          if array[i] < pivot:
               lowerCAmelCase_					:       Optional[Any]    =		True
               lowerCAmelCase_					:       Tuple    =		[element for element in array[i:] if element >= array[i]]
               lowerCAmelCase_					:       Any    =		longest_subsequence(_a			)
               if len(_a			) > len(_a			):
                    lowerCAmelCase_					:       List[Any]    =		temp_array
          else:
               i += 1

     lowerCAmelCase_					:       Tuple    =		[element for element in array[1:] if element >= pivot]
     lowerCAmelCase_					:       List[Any]    =		[pivot, *longest_subsequence(_a			)]
     if len(_a			) > len(_a			):
          return temp_array
     else:
          return longest_subseq


if __name__ == "__main__":
      import doctest

      doctest.testmod()
