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#
#......#
########

Example Output

YES
9
LDDRRRRRU