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

You are given a map of a labyrinth, and your task is to find a path from start to end. You can walk left, right, up and down.

# 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