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

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