Uolevi has been wandering around an abandoned warehouse recording his true-crime podcast. Getting purposefully lost is part of the fun: now he just needs to find a way out. Uolevi finds a map of the building on a wall. On the map, he can walk left, right, up, and down. Help Uolevi find a way out or report that he is locked in for good.

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 warehouse. Each character is . (floor), # (wall), A (Uolevi), or B (exit). There is exactly one A and one B in the input.

Output

In the first line, print "YES" if there is a way and "NO" otherwise.

If there is a path, print the length of the shortest such path on the next line and its description as a string consisting of characters L (left), R (right), U (up), and D (down) on another line. You can print any valid solution.

Constraints

• 1 \le n,m \le 1000

Example

Input:

5 8
########
#.A#...#
#.##.#B#
#......#
##..####

Output:

YES
9
LDDRRRRRU