The Rubik's Cube is one of the most famous mechanical puzzles in the world. In a
classic 3x3x3 Rubik's Cube, each of the six faces is covered by nine stickers,
among six solid colors (traditionally white, red, blue, orange, green and
We can name the six faces as F(Front), B(Back), U(Up), D(Down), L(Left), R(Right).
A letter followed by a prime symbol (') means rotating the corresponding face 90
degrees in counterclockwise direction, while a letter without a prime symbol
denotes a clockwise turn. A letter followed by a "2" denotes two turns, in other
words, a 180-degree turn.
One day, Hongshu performed a sequence of moves, which left the puzzle in a
scrambled state. After seeing that, Hongshu began to wonder whether repeating the
exact same sequence of moves over and over again would bring the cube back to its
initial state --- that is, each of the small stickers must return to the exact
same place where it started. Could you help him?
For each case, print an integer X in a single line, which is the smallest number
of rounds Hongshu need to perform all the rotations to bring each sticker to
where it was in the beginning(including the first round). If no such X exists,
print -1 instead.