_{This problem is a programming version of Problem 244 from projecteuler.net}

You probably know the game Fifteen Puzzle. Here, instead of field 4 by 4 and numbered tiles, we have field by , [] red tiles and [] blue tiles.

A move is denoted by the uppercase initial of the direction (Left, Right, Up, Down) in which the tile is slid, e.g. starting from configuration (S), by the sequence LULUR we reach the configuration (E):

(S)	(E)

For each path, its checksum is calculated by pseudocode:

...

where is the ASCII value of the -th letter in the move sequence and the ASCII values for the moves are:

For the sequence LULUR given above, the checksum would be .

Now, starting from given configuration (S), find all shortest ways to reach given configuration (E).

What is the sum of all checksums for the paths having the minimal length?