Vladik and Favorite Game
Contest: Codeforces Round 416 (Div. 2)
Difficulty rating: 2100
Tags: constructive algorithms, dfs and similar, graphs, interactive

This is an interactive problem.

Vladik has favorite game, in which he plays all his free time.

Game field could be represented as n × m matrix which consists of cells of three types:

- «.» — normal cell, player can visit it.
- «F» — finish cell, player has to finish his way there to win. There is exactly one cell of this type.
- «*» — dangerous cell, if player comes to this cell, he loses.

Initially player is located in the left top cell with coordinates (1, 1).

Player has access to 4 buttons "U", "D", "L", "R", each of them move player up, down, left and right directions respectively.

But it’s not that easy! Sometimes friends play game and change functions of buttons. Function of buttons "L" and "R" could have been swapped, also functions of buttons "U" and "D" could have been swapped. Note that functions of buttons can be changed only at the beginning of the game.

Help Vladik win the game!

Input format:
First line contains two space-separated integers n and m (1 ≤ n, m ≤ 100) — number of rows and columns respectively.

Each of next n lines contains m characters describing corresponding row of field. Set of characters in field is described above.

Guaranteed that cell with coordinates (1, 1) is normal and there is at least one way from initial cell to finish cell without dangerous cells.

Interaction format:
You can press buttons no more than 2·n·m times.

To press a button you should print "U", "D", "L", "R" in new line. It’s necessary to print newline character and flush output. After flushing buffer you should read answer from input data. Answer is the pair of space-separated integers x, y — new position of player. In case, if there is no cell in direction of moving, position will not change. If after any move player lost, in other words player move to dangerous cell, then x and y will be equal to  - 1.

If after any move player is in finish or dangerous cell, then you should terminate your program.

To finish output buffer (i. e. for operation flush) right after printing direction and newline you should do next:

- fflush(stdout) in C++
- System.out.flush() in Java
- stdout.flush() in Python
- flush(output) in Pascal
- read documentation for other languages.

Hacks

To perform a hack you should use this format:

Where n, m — number of rows and columns in game field. swapLR is equal to 1 in case, when directions "L’’ and "R’’ is swapped, and equal to 0 otherwise. swapUD is equal to 1, when directions "U’’ and "D’’ is swapped, and equal to 0 otherwise. a1, a2, ..., an — description of corresponding rows of game field.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
In first test case all four directions swapped with their opposite directions. Protocol of interaction In more convenient form:

This test could be presenter for hack in following way:

Example input:
4 3
...
**.
F*.
...
1 1
1 2
1 3
1 3
2 3
3 3
4 3
4 2
4 1
3 1

Example output:
R
L
L
D
U
U
U
R
R
D

Editorial:
It's clear, that to reach finish without stepping into dangerous cells we have to know, whether our buttons are broken. Firstly, let's find any route to the finish using bfs / dfs. At the first moment of this route, when we have to go down, we would find out, if our button is broken, because we are still at the first row of the matrix and if the button is broken, we just won't move anywhere. Similarly for left and right pair of buttons. After that we found out, that button was broken, we can change in our route moves to opposite ones.