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

**Input**

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

Then there are $n$ lines of $m$ characters describing the labyrinth. Each character is

`.`

(floor), `#`

(wall), `A`

(start), or `B`

(end). There is exactly one `A`

and one `B`

in the input.**Output**

First print "YES", if there is a path, and "NO" otherwise.

If there is a path, print the length of the shortest such path and its description as a string consisting of characters

`L`

(left), `R`

(right), `U`

(up), and `D`

(down). You can print any valid solution.**Constraints**

- $1 \le n,m \le 1000$

**Example**

Input:

`5 8`

########

#.A#...#

#.##.#B#

#......#

########

Output:

`YES`

9

LDDRRRRRU