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CSES Problem Set

Monsters


Task | Statistics


CSES - Monsters

Time limit:1.00 s Memory limit:512 MB

You and some monsters are in a labyrinth. Always when you move one step, each monster may also move one step. Your goal is to reach one of the boundary squares so that you will never be in the same square with a monster.

Your task is to find out if your goal is possible, and if it is, print a path that you can follow. Your plan has to work in every situation; even if the monsters know your path beforehand.

Input

The first input line has two integers $n$ and $m$: the height and width of the map.

After this there are $n$ lines of $m$ characters that describe the map. Each character is . (floor), # (wall), A (start), or M (monster). There is exactly one A in the input.

Output

First print "YES" if your goal is possible, and "NO" otherwise.

If your goal is possible, also print an example of a valid path (the length of the path and its description using characters D, U, L, and R. You can print any path, as long as its length is at most $n \cdot m$ steps.

Constraints
Example

Input:
5 8
########
#M..A..#
#.#.M#.#
#M#..#..
#.######


Output:
YES
5
RRDDR