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Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Goal

Given a configuration of the Rubik's cube, find its doubly solved configuration. Specifically, pick any sequence of twists that solves the given Rubik's cube. Apply that same sequence twice to the given cube (once to solve it, then again to get some new configuration). You are asked to output the resulting configuration.

It can be shown that the result is independent of the sequence of twists used to solve the initial cube. In this problem only the configuration below counts as solved (no other orientations).

The solved cube configuration is:
    UUU    UUU    UUULLL FFF RRR BBBLLL FFF RRR BBBLLL FFF RRR BBB    DDD    DDD    DDD
There are no trailing spaces.
Input
A flattened Rubik's cube configuration. If we made a cut-out of the flattened configuration on paper, we could fold the flaps backwards to produce a cube. This gives each input character a corresponding Rubik's cube sticker.

3 lines: The top of the cube
Blank line
3 lines: The left, front, right and back of the cube
Blank line
3 lines: The bottom of the cube
Output
The doubly solved configuration in the same format as the input.
Constraints
The input will be a valid cube configuration, i.e. it can be solved by a sequence of twists and full cube orientation changes.
Example
Input
    UUF
UUF
UUF

LLL FFD RRR UBB
LLL FFD RRR UBB
LLL FFD RRR UBB

DDB
DDB
DDB
Output
    UUB
UUB
UUB

LLL FFU RRR DBB
LLL FFU RRR DBB
LLL FFU RRR DBB

DDF
DDF
DDF

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