Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Shift It!

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere is a square box 6 × 6 in size. It contains 36 chips 1 × 1 in size. Those chips contain 36 different characters — "0"-"9" and "A"-"Z". There is exactly one chip with each character.

You are allowed to make the following operations: you may choose one of 6 rows or one of 6 columns and cyclically shift the chips there to one position to the left or to the right (for the row) or upwards or downwards (for the column). Those operations are allowed to perform several times.

To solve the puzzle is to shift the chips using the above described operations so that they were written in the increasing order (exactly equal to the right picture). An example of solving the puzzle is shown on a picture below.

Write a program that finds the sequence of operations that solves the puzzle. That sequence should not necessarily be shortest, but you should not exceed the limit of 10000 operations. It is guaranteed that the solution always exists.

Input

The input data are represented by 6 lines containing 6 characters each. They are the puzzle's initial position. Those lines contain each character from the string "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" exactly once.

Output

On the first line print number *n*, which is the number of operations. On the next *n* lines print the sequence of operations one per line. An operation is described by a word consisting of two characters. The first character shows the direction where the row or the column will be shifted. The possible directions are "L", "R" (to the left, to the right correspondingly, we shift a row), "U", "D" (upwards, downwards correspondingly, we shift a column). The second character is the number of the row (or the column), it is an integer from "1" to "6". The rows are numbered from the top to the bottom, the columns are numbered from the left to the right.

The number of operations should not exceed 10^{4}. If there are several solutions, print any of them.

Examples

Input

01W345

729AB6

CD8FGH

IJELMN

OPKRST

UVQXYZ

Output

2

R2

U3

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/26/2018 06:49:11 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|