Problem Statement

One day, E869120 the Coder went to "AtCoder Natural Park".
The park represented as H*W grid. The top-left corner cell is (1,1) and the bottom-right corner cell is (H,W).
In addition, N gems drop in the park. In each cell, there are no more than 1 gem drops.

He want to collect all gems in the park.
He have "special smell-sense", so if there are 1 or more gems in relative-position that he decide beforehand, he think that "there is a gem near me".
The example of "relative position" is as follows:

In the left picture, if E869120 exists in the cell (4, 4), gems in cell (6, 5) and (2, 4) is "near". Suppose his relative position is (0, 0). In this case, the relative position of gem in example is (2, 1) and (-2, 0) in order. To see the picture, both (2, 1) and (-2, 0) is near.
But (2, 3) isn't near because its relative position is (-2, -1) and it is not near as long as see the picture.

However, he can move to one of 4-adjacent cells which share a side in 1 second. If there is a gem on the cell that E869120 exists, he pick it automatically in 0 second.
Initially, he is on the cell (1, 1). Please write the program that collect all gems in the park as fast as possible.

Input and Output

This problem is "interactive task" (the task which has to take communications with input and output of program), so the format of input/output is special.

First, you are given the size of "AtCoder Natural Park": H and W. You are also given the number of gems: N. The input format is as follows:

H W N

Second, you must set the relative-direction which includes "near", to make E869120's "special smell-sense".

P
x_1 y_1
x_2 y_2
...
x_P y_P

In the 1-st line, you should output the number of relative-position which include "near": P. 0 \leq P \leq 500 should be satisfied.
From the 2-nd line to P+1-th line, you should output relative-position: (x_i, y_i). x_i,y_i should be greater than -10^9 and less than 10^9. If there is gem on the cell that E869120 exists, he pick it instantly. So, (x_i, y_i) should not be (0, 0).

Next, it repeats the following two processes (☆) and (★) alternately (the first process is (☆)).

(☆) You are given an information as follows:

S

The information is classified as follows:

• far: There is no gems in his cells. In addition, there is no gem in relative-position that you set.
• close: There is no gems in his cells. In addition, there is 1 or more gems in relative-position that you set.
• get-far: There is a gem in his cells, so E869120 picks it. In addition, there is no gem in relative-position that you set after he picks.
• get-close: There is a gem in his cells, so E869120 picks it. In addition, there is 1 or more gems in relative-position that you set after he picks.
• get-clear: There is a gem in his cells, so E869120 picks it. In addition, all gems collected. You have to terminate your program if you program is given get-clear.

(★) E869120 moves. You should print as follows:

c

• If c is L, it means he moves to the left cell.
• If c is R, it means he moves to the right cell.
• If c is U, it means he moves to the up cell.
• If c is D, it means he moves to the down cell.
• He should not move to outside of the park.

Scoring

There are 15 testcases in this problem. For each cases, the max score is 100 points.
Let L be the number of moves. The point is calculated as follows:

• If L \leq 2 \ 100, 100 points.
• If 2 \ 101 \leq L \leq 2 \ 260, floor(100 - \frac{L - 2100}{8}) points.
• If 2 \ 261 \leq L \leq 2 \ 540, floor(80 - \frac{L - 2260}{14}) points.
• If 2 \ 541 \leq L \leq 3 \ 000, floor(60 - \frac{L - 2540}{25}) points.
• If 3 \ 001 \leq L \leq 5 \ 000, floor(41.6 - \frac{L - 3000}{125}) points.
• If 5 \ 001 \leq L \leq 6 \ 000, 24 points.
• If 6 \ 001 \leq L \leq 7 \ 000, 21 points.
• If 7 \ 001 \leq L \leq 8 \ 000, 18 points.
• If 8 \ 001 \leq L \leq 9 \ 000, 15 points.
• If 9 \ 001 \leq L \leq 10 \ 000, 3 points.

The graph that represents the correlation between the number of moves and score is as follows:

Sample Input and Output

The state of the park and the relative direction that includes "near" is as follows:

The interaction between computer and judge is as follows: