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.

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.

• $1 \le n,m \le 1000$

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.