Sliding Puzzle solver

Problem code: SSLIDE
----------------------

Given a initial position of a sliding puzzle determine the moves to arrange them back in order.(A number can be swapped only with x)

Initial position

1 2 3
4 5 x
6 7 8

Final position

1 2 3
4 5 6
7 8 x

Input

Intial position of the puzzle

1 2 3
4 5 x
6 7 8

is described as 1 2 3 4 5 x 6 7 8

Output

If it has no solution print unsolvable.
If it has a solution print a string describing the sequence of moves that has to be performed on the puzzle to solve it. (l-left,r-right,u-ip,d-down)

Example

Input:
1 2 3 4 5 x 6 7 8

Output:
dllurdrulldrr

<<Solution development In progress>>