Practice Geometry with the exercise "1×1×1 Rubik’s cube movements"

Learning Opportunities

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

Geometry

Statement

Goal

A 2×2×2 Rubik's cube is quite complicated. In this puzzle, we will focus on the mono-cube, the 1×1×1 Rubik's cube!

You are given a set of rotations and two faces. Apply the rotations to the cube and locate the two faces after the rotations.

Face notation
F (Front): the side currently facing the observer
B (Back): the side opposite the front
U (Up): the side above or on top of the front side
D (Down): the side opposite the top, underneath the cube
L (Left): the side directly to the left of the front
R (Right): the side directly to the right of the front

Rotation notation
A rotation without the prime symbol ' is a quarter turn clockwise.
A rotation with the prime symbol ' is a quarter turn counter-clockwise.
x, x': rotate cube on R (R and L still face the same directions after rotation)
y, y': rotate cube on U (U and D still face the same directions after rotation)
z, z': rotate cube on F (F and B still face the same directions after rotation)

Example 1
z
D
L
Means: rotate cube clockwise on F and identify the new directions of D and L.
Answer: Output L in line 1 because the initial down face now faces left. Output U in line 2 because the initial left face now faces up.

Example 2
z z'
U
R
Means: rotate cube clockwise on F then counter-clockwise on F, and identify the new directions of U and R.
Answer: Output U in line 1 and R in line 2 because both faces do not change directions after the rotations.

Input

Line 1: Space-separated rotations in xyz notation.
Line 2: Initial direction of face1 the first queried face.
Line 3: Initial direction of face2 the second queried face.

Output

Line 1: Direction of face1 after the rotations.
Line 2: Direction of face2 after the rotations.

Constraints

1 ≤ length of rotations ≤ 100

Example

Input

z
D
L

Output

L
U

Solve it

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