Monsters

• Time limit: 1.00 s
• Memory limit: 512 MB

You and some monsters are in a labyrinth. When taking a step to some direction in the labyrinth, each monster may simultaneously take one as well. Your goal is to reach one of the boundary squares without ever sharing a 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 any 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 describing 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

• $1 \le n,m \le 1000$
  

Example

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

Output:
YES
5
RRDDR