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ZOJ Problem Set - 4093
Robot Cleaner II

Time Limit: 1 Second      Memory Limit: 65536 KB      Special Judge

(Please read the description of Robot Cleaner I first.)

Tired of programming the robot every time according to the situation of his room, BaoBao decides to write a "super program" so that the robot can pick up most of the litter using this program, no matter how the litter is positioned in the room.

To simplify this problem, we now put some constraints on BaoBao's room and the robot.

  • $n = m = 12$;
  • For all $1 < i < n$ and $1 < j < m$, $(i, j)$ is NOT a wall;
  • There are exactly 50 pieces of litter in the room, and they are randomly distributed with equal probability;
  • The robot always starts from $(2, 2)$.

Your task is to design the "super program", so that when feeding this program to the controller, the robot can pick up at least 95% of the litter in the room under the above constraints after executing 200 instructions.

Input

There is no input for this problem.

Output

You should output a string of length 243 ($243 = 3^5$) consisting of 'U', 'D', 'L', 'R', 'P' and 'I' in one line, indicating your super program.

Sample Output

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Hint

Note that this output example is (obviously) NOT the correct answer. It only serves the purpose of showing you the output format.

We have prepared 1000 randomly generated rooms under the above constraints and will test your solution against them. Your solution will be accepted if the robot can pick up at least 95\% of the litter on average in these 1000 rooms after executing 200 instructions in your super program.


Author: WENG, Caizhi
Source: The 19th Zhejiang University Programming Contest Sponsored by TuSimple
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